Institute of Risk http://www.liv.ac.uk/risk-and-uncertainty PhD Project ...

Institute of Risk 

http://www.liv.ac.uk/risk-and-uncertainty 

PhD Project for promotion to students who bring their own funding 

Name of Project: Integrated Risk Analysis and Risk-based Design 

Supervisor (s): Michael Beer (Engineering) and Laurence Alison (Psychology) 

further co-supervision depending on student’s background and interest 

Outline of Project: 

In the assessment of risks it is not only important to include technical issues in a realistic 

manner, but it is also of interest how the risks are perceived by the users or the society in 

order to specify a reasonable risk acceptance level. This includes an integration of the 

society in the determination of technical solutions, in particular, when high-consequence 

risk issues are involved. Technical solutions which are not in balance with societal 

acceptance can lead to large-scale problems with severe consequences even on an 

international economic and political level. These problems can be associated with technical 

issues and with issues in the information exchange with the society. Recent examples are 

the nuclear disaster in Fukushima and the oil spill in the Gulf of Mexico but also the disputes 

in the discourse of the construction project Stuttgart 21. In the latter case, a solution could 

be achieved in a heuristic manner via information exchange with the society. 

This project is devoted to developing a systematic approach for a comprehensive 

integration of both technical issues and societal issues into risk analysis and risk-based 

design. The first stage is focused on the investigation of the interaction between the 

technical component and the societal component in the specification of acceptable risks for 

selected classes of engineering structures and systems. In the second stage, it is envisaged 

to develop a strategy and an algorithm for decision-making in engineering design with 

critical risk issues. Technically, this is a multi-criteria optimization problem of high 

complexity and involving various forms of uncertainties. This combination requires nonstandard 

optimisation approaches and generalised uncertainty models for solution. 

Any special features: (e.g. equipment, collaboration, industrial links, underpinning 

expertise) 

The project requires a sound mathematical background, curiosity, creativity and a strong 

interest to work in a multi-disciplinary set-up. Applicants should have a background in 

Engineering (preferably Civil or Systems Engineering) or in relevant fields from Social Science 

or Psychology. A combined education in these fields would be an advantage. 

The student will join a multi-disciplinary research group in the Institute for Risk and 

Uncertainty. 

Funding details: Self funding 

Starting Arrangements: start date as soon as possible

Restrictions on student nationality: None 

For further details, please send a copy of your curriculum vitae to either Professor Michael 

Beer (email: mbeer@liverpool.ac.uk) or Professor Laurence Alison 

(l.j.alison@liverpool.ac.uk). 

PhD Project for promotion to students who bring their own funding 

Name of Project: Risk mitigation: human errors and preventive design and project 

management 

Supervisor (s): Michael Beer (Engineering), Franz Knoll (Engineering / Industry), Jan 

Wenzelburger (Economics, Finance), further co-supervision depending on 

student’s background and interest 


Human errors are a major reason for faults and flaws in structures, industrial systems, 

products and for associated economic losses on an individual, societal and business level. 

These errors include lack of attention, communication, competence etc. Even where 

natural events are implied as causes of loss such as storms, earthquakes or flooding, human 

intervention is found to contribute to the mishap by failing to properly account for their 

effects. In some cases, human behaviour is even the triggering agent, through 

anthropogenic changes. Causes of losses through manifest accidents, or due to costs of 

belated corrections of flaws, are mostly found in structural or physical weaknesses of the 

constructions themselves which have their origin in errors committed in the building 

process which were not caught and corrected in time. It is here that activities such as 

controls, checking, surveillance, verification, validation, auditing etc come to bear. Since 

these activities are organized and carried out by humans, the competence of the people 

involved becomes an important parameter relating to education as well as personal 

qualifications such as dedication, attention and circumspection. It is, thus, of paramount 

importance to develop and include the economics of asymmetric information into the 

optimization process for risk mitigation and reduction. These considerations must include 

error proneness, magnitude of risk, timing, appropriation of resources etc. 

This project is devoted to approach this comprehensive and complex challenge in a 

systematic manner. Starting point is a large-scale analysis of human errors based on real 

projects from around the world. The systematic analysis will provide implications for both 

improving the robustness of structural and system design from a technical perspective and 

an economic perspective. The implications will then be translated into a robust organization 

of design and control in order to minimize economic losses due to human errors in real 

projects. In order to achieve stimulus for industry implementation of the development, 

insurance and re-insurance companies as well as experts involved in sorting out the 

consequences of errors will be asked to provide data on real cases. Collection of data will 

be followed by the development of appropriate mathematical methods to interpret the

data, to gain insight into the circumstances leading to the genesis and perpetuation of 

errors and to find strategies to eliminate or mitigate their effects. 


expertise) 

The project requires a sound civil or systems engineering background, curiosity, creativity 

and a strong interest to work in a multi-disciplinary set-up. Applicants should also have a 

strong background in mathematics and economics/finance or related areas. A combined 

education in two or more areas would be advantageous. 

The student will join a multi-disciplinary research group at the Institute for Risk and 

Uncertainty. 


Starting Arrangements: start date as soon as possible 



Beer (email: mbeer@liverpool.ac.uk) or Professor Jan Wenzelburger 

(jwenzelb@liverpool.ac.uk). 

Name of Project: Uncertainties and Risk from Environmental Changes 

Supervisor (s): Michael Beer (Civil Engineering) and Ioannis Kougioumtzoglou (Civil 

Engineering) 



This project is focussed on environmental changes and associated risks for Civil Engineering 

structures and infrastructure. This includes the implementation of climate change effects in 

numerical models for environmental loads as well as an analysis of their impact on the 

performance and reliability of selected structures and systems. A consideration of 

consequences in the case of failure supplements the research from a risk point of view. The 

envisaged research is motivated by the evident changes in our environment, which resulted 

in an increase of damage due to extreme events such as storms and floods. Starting point is, 

thus, the entire database available from climate prediction – climate change prediction itself 

is not pursued. Relevant non-stationarities and further essential characteristics need to be 

analyzed and translated into probabilistic engineering load models. This requires the 

analysis of rare and imprecise data with sophisticated methods from mathematical statistics 

and computer science. Potential benefits from the improved load models are investigated in 

subsequent reliability and risk analyses. 


expertise)



Engineering (preferably Civil or Systems Engineering) or in relevant fields from Mathematics 

or Computer Science. Programming Skills are essential. 


Uncertainty. 





Beer (email: mbeer@liverpool.ac.uk) or Dr. Ioannis Kougioumtzoglou 

(kougioum@liverpool.ac.uk). 

Name of Project: Drought Risk 

Supervisor (s): Michael Beer (Engineering) and Neil Macdonald (Environmental Sciences) 



Whilst considerable work has focused on the risks and uncertainties associated with 

flooding, risks from droughts are often underestimated. This proposal would address this 

issue by developing a better understanding in drought magnitude, frequency and severity; 

whilst the approaches used in assessing drought magnitude are similar to the approaches 

used in examining floods, the frequency and severity of droughts require different 

approaches. Droughts are not characterised as discrete events in the manner that flood can 

be considered, as droughts are cumulative and the severity of a drought is not simply a 

reflection of the magnitude, but also the duration, as such any assessment of frequency 

needs to consider this. Previous research examining droughts have predominantly focussed 

on climate models and predictions, which fail to examine the wealth of long records often 

available from which drought indices can be generated. This research will use specific 

drought indices in the form of the Palmer Drought Severity Index (PDSI) and Standardised 

Precipitation Index (SPI) to derive long drought indices from which new models of analysis 

can examine the uncertainties and risks associated with droughts. 

For a realistic prediction of droughts we aim at developing a suitable and powerful 

numerical model. From a mathematical point of view the occurrence of droughts appears as 

a random process with quite significant memory features. These memory features refer, in 

particular, to the cumulative characteristics of the drought phenomena. This excludes the 

utilisation of the commonly used and well-established Markov type models for process 

simulation and prediction. It is essential to analyse the process memory and to implement it 

in the numerical process model for droughts. The process model must, further, be

formulated in the context of climate data, such as precipitation and temperature, and it 

must be able to reflect non-stationarity due to climate change effects. Stochastic process 

models for numerical simulation which satisfy these requirements ad hoc are not available. 

Our development will start from a probabilistic modelling of physical mechanisms as far as 

these are known, utilise conditional physical input from available climate models and 

supplement this basis by statistical means. For modelling in time-frequency domain, wavelet 

transform appears as most promising as it basically provides the flexibility required. To cope 

with complexity and limited physical insight, neural networks provide a promising module 

for the process model as sufficient data are available for their training. Remaining model 

uncertainty, for example in the climate prediction and in dependencies and memory 

features, can be addressed with methods of imprecise probabilities. Imprecise probabilistic 

models cover an entire set of plausible probabilistic models and help to reduce the risk of 

missing critical situations. 

The outputs of this work are considerable as they will contribute significantly to better 

policy development and risk assessment in water resource management. 


expertise) 



Engineering (preferably Civil or Systems Engineering) or in relevant fields from 

Environmental Sciences. A combined education in these fields would be an advantage. 


Uncertainty. 





Beer (email: mbeer@liverpool.ac.uk) or Dr. Neil Macdonald (nim@liverpool.ac.uk).

Name of Project: Efficacious Signal Processing Techniques for Risk Assessment of Civil 

Infrastructure subject to Natural Hazards 

Supervisor (s): Ioannis Kougioumtzoglou (Engineering) and Michael Beer (Engineering) 



Structural systems are often subject to natural and man-made hazards and to extreme 

events due to climate change, such as seismic motions, winds, ocean waves, impact and 

blast events, hurricanes, storms and floods, which inherently possess the attribute of 

evolution in time. Further, structures can become nonlinear and inelastic with restoring 

forces depending on the time history of the response under severe time-varying excitation 

(i.e. exhibit hysteresis). Therefore, representation of these complex phenomena by nonstationary 

stochastic processes is necessary to capture accurately the system/structure 

behaviour. Although several research efforts have focused on determining the response of 

nonlinear systems, limited results exist in the context of a joint time-frequency analysis. 

Further, it is noted that the envisaged research project is largely motivated by the evident 

changes in our environment and their consequences (see the recent Stern report). In this 

context, extreme events related to climate change can cause major losses, and thus, the 

issue of risk/uncertainty quantification arises in many activities. It may emanate from an 

inevitably incomplete understanding of infrequent climate change events to failure in 

recognising what fragilities might exist in systems/structures. These extreme events have 

increased the exposure of public and private services to risk. As a consequence, decision 

makers are challenged to assess exposure to risk and to identify risk emergent events. 

In this research project, the available database related to natural hazards will be utilized to 

translate the raw data into useful probabilistic engineering excitation models. To this aim, 

advanced signal processing methodologies will be developed for determining the content 

and quantifying the uncertainty of (most often) irregularly sampled data with missing 

observations. Further, joint time-frequency response analyses will be performed based on 

the localization capabilities of the wavelets and of other newly proposed potent transforms. 

Subsequent applications will include risk quantification and reliability assessment of 

buildings, bridges and related infrastructure utilities following complex hysteretic behaviour 

and subjected to natural hazards such as extreme events due to climate change (e.g. storms, 

floods and hurricanes). 


expertise) 

The project requires a strong mathematical background and a keen interest to work in the 

interface of signal processing and probabilistic engineering mechanics. Applicants should 

have a background in Engineering (preferably Civil, Mechanical, Aerospace or Naval/Marine 

Engineering) or in relevant fields from Mathematical Sciences. A combined education in 

these fields would be an advantage. 

The student will join a multi-disciplinary research group in the Institute for Risk.


Starting Arrangements: start date as soon as a student is found 


For further details, please send a copy of your curriculum vitae to either Dr. Ioannis 

Kougioumtzoglou (kougioum@liverpool.ac.uk) or Professor Michael Beer (email: 

mbeer@liverpool.ac.uk) 

Name of Project: Stochastic Modelling and Analysis of Catastrophe (CAT) Bond Products 

Supervisor (s): Ioannis Kougioumtzoglou (Engineering) and Athanasios Pantelous (Financial 

and Mathematical Sciences); further co-supervision depending on student’s background and 

interest 


The proposed multi-disciplinary research project focuses on the areas of financial science, 

engineering and mathematics. In general, the financial stability and social sustainability at a 

national and international level are always susceptible to the influence of various natural 

hazards. This project will be a groundbreaking attempt to design catastrophe (CAT) bond 

products for both earthquake and tsunami risks affecting populous cities, or/and industrial 

areas. In this regard, the insurance and reinsurance industries have been constantly looking 

for alternative ways to spread the risk, especially for such large insured losses (e.g. Swiss Re 

estimates claims costs of USD 1.2 billion, net of retrocession and before tax for Fukushima 

incident, Japan 2011; see released report on the 21 st of March 2011). Further, the potential 

of the developed instruments as mechanisms for transferring hazard risks from insurance 

and re-insurance companies to investors/speculators in the global capital markets will also 

be examined. Specifically, individual objectives of the project will include: 

a) Identification and quantification of the most significant parameters which describe 

the natural hazards such as location, magnitude, maximum surface acceleration, loss 

frequency of damages, loss frequency of earthquake - related fires, loss frequency of 

damage due to tsunami etc. 

b) The adoption of various securitization issues and the new Solvency II regulations 

which are currently being used by Swiss Re and others. 

c) The development of a stochastic model for the discount interest rate parameter (e.g. 

Euribor rate). In this manner, the potentials of stochastic mechanics tools and 

concepts developed from an engineering perspective will be exploited. It is envisaged 

that they will offer a unique new insight and means to address complex problems in 

the interface of financial and engineering applications. Next, further analysis and 

development of the model will be sought to allow pricing CAT bonds in a nontradable 

(incomplete) market framework.

For training and prototype development in this virgin field the specific case of the 

Fukushima nuclear power plant incident will be considered in detail as an application 

example. The insurance and reinsurance industries will be greatly benefited by the research 

outcomes of the proposed project which will contribute towards more reliable risk 

assessment and enhanced decision making procedures. 


expertise) 


interface of financial mathematics and probabilistic engineering mechanics. Applicants 

should have a background in Engineering (preferably Civil, Mechanical, or Naval/Marine 

Engineering) and/or in relevant fields from Mathematical and Financial Sciences. A 

combined education in these fields would be an advantage. 

The student will join a multi-disciplinary research group in the Institute for Risk. 





Kougioumtzoglou (email: kougioum@liverpool.ac.uk) or Dr. Athanasios Pantelous (email: 

aap@liverpool.ac.uk). 

Extending current flood risk estimates through the incorporation of sedimentary archive 

data and reanalysis using novel statistical techniques 

Beer M (Engineering), Macdonald N & Plater A (Environmental Sciences) & Horsburgh K 

(NOC) 

Proposal: Conventional flood risk estimates are derived from instrumental data series 

collected from around the British coastline. Whilst these series are relatively long on a 

global scale, they are from an extreme flood analysis perspective relatively short, 

particularly when considering return frequencies of >100 years. Unfortunately, the 

conventional data are constrained by short measurement periods; as such thresholds for 

the purpose of extreme flood estimation are uncertain and potentially erroneous. Whilst 

historical and, increasingly, sedimentological data are being used widely in refining fluvial 

flood risk, few studies have considered the potential value of sedimentological data in 

improving estimates of coastal flood risk, particularly from extreme coastal events (an 

exception being Baart et al., 2011). This project will integrate instrumental, historical and 

sedimentary records on a quantitative basis to improve the database of flooding for the last 

2000 years, refining the flood history for South-east England. By developing an advanced 

toolkit, the approaches applied will incorporate a better understanding of archive 

approaches, developing and testing a robust methodology for the wider application of using

integrated historical and sedimentary evidence to refine estimation of flood risk. This 

studentship would seek to investigate the opportunities for reassessing high magnitude 

flood risk in the Thames estuary, an area of particular interest given the development of the 

Thames Gateway project and the second generation Thames Barrier. A detailed historical 

record of flooding exists for the area and also offers high potential for sedimentological 

preservation and therefore record reconstruction. The incorporation of these sources into 

the flood risk assessment will also provide additional information which can be considered 

within the remit of a changing climate. Data and information involved in the flood risk 

estimates are of an inconsistent and incomplete nature combined with the rare occurrence 

of extremes. These features represent major obstacles for a statistical analysis in two 

respects. First, the question of modelling epistemic uncertainty and of including respective 

imprecise and vague information into a statistical analysis and estimation needs to be 

answered. Second, the problem of rare data and information needs a proper solution to 

obtain suitably precise estimates. The solution requires a mixture of evolving methods and 

techniques from engineering and mathematical statistics. Dealing with inconsistent data and 

information in engineering, models of imprecise probabilities have attracted increasing 

attention in the recent past and have shown appealing features for the solution of 

associated problems. Probably the most advanced and powerful model in this context is 

fuzzy probability theory. This provides a simultaneous consideration of both epistemic and 

aleatory uncertainties in one sound mathematical model without mixing their natural 

characteristics. Imprecision, vagueness, indeterminacies etc. are managed via intervals and 

fuzzy sets and do not migrate into probabilities, but become visible in the results. In view of 

estimating extremes based on rare data advancements has been reported using nonparametric 

estimators in combination with a data transformation. In addition, techniques 

for utilizing dependencies between related data sets have been successfully tested to 

conclude extreme statistics from non-extreme data in a related sample. The environmental 

data under consideration exhibit features, which call for both approaches. 

Programme of research: Three data sources (instrumental, documentary and sedimentary) 

will be targeted to recover independent evidence for extreme floods, which can then be 

integrated into flood frequency analysis. Coupling of the archival and sedimentary record is 

dependent on the determination and dating of flood layers in alluvial sequences and 

estimation of flood magnitude, this will be undertaken through calibration within the 

instrumental/historical timeframe. [1] Estuarine areas display numerous sedimentary sinks 

which infill. Cores from these infills comprise typically alternating silty and sandy facies, with 

coarser layers generally reflecting floods. Particle size, geochemical and magnetic analysis of 

the marine sediments will be undertaken to discern changes in the proxy records that relate 

to discharge and extreme events, thereby allowing the identification of historical flood 

deposits. [2] Robust chronologies for the sedimentary archives will be secured, employing 

radiocarbon dating (funding sought through the NERC radiocarbon laboratory). Careful 

correlation of flood layers in alluvial sediments with historical floods identified from 

documentary sources will improve understanding of flood frequency and potentially 

indicate event magnitude. Critically calibration and correlation of these archives for the 

recent record will improve confidence in the interpreted flood signal permitting robust 

chronological (age-depth) models for the longer proxy record (sediment) to be used to 

extend the evidence for flooding to the much needed period (~2000 years) before historical 

and measurement records. [3] These results will be the basis for the development of a novel

statistical approach for extreme flood prediction. Dependencies between the different kinds 

of information are analysed in order to identify the most significant statistical mechanisms 

and possibly a data transformation scheme. This will allow implementations to exploit 

available information to a maximum extent. On the other hand, to not introduce 

unwarranted information, indeterminacies and missing information in this analysis are 

covered by imprecise mathematical formulations using fuzzy sets, which are then 

implemented into the derived probabilistic models and estimates via fuzzy probabilities. In 

this manner, the extreme flood estimates will cover the entire range of plausible predictions 

using an entire set of plausible probabilistic models. Additional data/information collected 

afterwards can be implemented into the new prediction model to naturally decrease the 

epistemic uncertainty in the form of imprecision in the estimates with the growing amount 

of information. The predictions from this envisaged model will exhibit a significantly better 

quality estimate compared to current practice and avoid facing unforeseen scenarios due to 

modelling errors. 

Name of Project: Robust design of financial market tools 

Supervisor(s): Edoardo Patelli (Engineering) 

Jan Wenzelburger (Management) 

Further co-supervision depending on student’s interest 

Outline of Project: The proposed multi-disciplinary research project combines 

engineering, financial science and mathematics. The last two decades has seen 

a severe increase in natural and technological disasters, the Fukushima incident 

being a prominent example. As consequence, insurance and reinsurance 

industries are exposed to increasing risks. In this regard, the insurance and reinsurance 

industries have been constantly looking for alternative ways to spread the risk, especially for 

such large insured losses. A better understanding of how to manage these risk Financially 

and how to design robust financial tool is of fundamental importance. 

The key stakeholders in the risk management of risk of natural hazards can be described by 

a pyramid where at the bottom are the property owners who are the primary victims of 

losses caused by hazards. Insurers on the next layer offer coverage to property owners 

against losses. However, faced with the possibility of very large claims caused by 

catastrophic events, insurers will turn to reinsurers, the next layer of the pyramid, to 

transfer some of their risk. Finally, at the top of the pyramid are the capital markets, which 

in recent years have provided financial protection to both insurers and reinsurers through 

financial instruments, such as Catastrophe (CAT) Bonds. 

In general, the magnitude of economic and insured losses from natural disasters raises 

various questions. For instance: a) who are the individuals affected by these events? b) 

What options are available to them to assess their risks? c) what factors influence their 

choices to deal with and actively managing these risks? 

The specific objectives of the project comprise the following: 

� Develop a reliability framework for modelling and analyse how hazard risks 

propagate into the financial market studying the impact of securitized risks on the 

prices of financial assets.

� Adopt the concept of robust design used extensively in engineering (especially 

regarding reliability theory) to analyse and evaluate the financial stability of the 

insurers, reinsurers and the entire financial market with respect to hazard risks. 

� Analyse the implications for the risk management of (re-)insurers as well as for the 

regulatory framework of financial markets (Basle III) and insurance markets 

(Solvency II). 

The insurance and reinsurance industries will be greatly benefited by the research outcomes 

of the proposed project which will contribute towards more reliable risk assessment and 

enhanced decision making procedures. 


expertise) 


interest to work with a multi-disciplinary research group. Applicants should have a 

background in Engineering or in relevant fields from Economics, Finance and accounting. 


Uncertainty. 

For further details, please send a copy of your curriculum vitae to either Dr. Edoardo Patelli 

(email: edoardo.patelli@liverpool.ac.uk) or Prof. Jan Wenzelburger 

(j.wenzelburger@liverpool.ac.uk) 

Name of Project: Robust Design of structures and systems 

Supervisor(s): Edoardo Patelli (Systems Engineering) 


Michael Beer (Structural Engineering) 

Further co-supervision depending on student’s background and interest 

This project targets at the development of numerical methods for robust design. The 

realistic consideration of uncertainties of various nature and scale is a key issue of this 

development to ensure a faultless life of engineering structures and systems despite 

fluctuations and changes of structural and environmental parameters and conditions. At the 

same time, consequences of unexpected events have to be minimized, and decision margins 

for subsequent design revisions have to be provided. This complexity requires both 

probabilistic and set-theoretical approaches to be considered. The focus is on both Civil 

Engineering structures and Engineering Systems, which may later be extended to further 

engineering fields as appropriate. The ultimate goal is a generally applicable numerical 

algorithm for comprehensive robust design cast in a software solution. The outcome of the 

project is expected to contribute significantly to developments towards sustainability in 

engineering design. 


expertise)


interest to work in a multi-disciplinary set-up. Applicants should have a background in Civil 

or Systems Engineering or in other relevant engineering or mathematical / computer 

science fields. Programming Skills are essential. 


Uncertainty. 





Beer (email: mbeer@liverpool.ac.uk) or Dr. Edoardo Patelli (email: 

edoardo.patelli@liverpool.ac.uk) 

Name of Project: Probabilistic risk assessment for multiple and simultaneous failures 

Supervisor(s): Edoardo Patelli (Engineering), 


Further co-supervision depending on student’s background 

and interest 

Climate changes may causing increasing of extreme weather events in different 

countries. In particular some recent studies have shown that climate change is 

already causing extreme weather such the increased risk of flooding in the 

United Kingdom. Despite all efforts and advances in security, severe weather can trigger 

multiple failures of technological installations (e.g. chemical plants, nuclear facilities, power 

grids, etc.) and consequently becoming a serious hazard for the population and the 

environment. 

Natural disasters have the potential to trigger simultaneous technological failures (cascade 

failures) from single or multiple sources. For instance, the management of nuclear power 

plants need to known the parts of their facilities where a natural hazards could lead to 

facility shut-down or in the worst case, core damage and release of hazardous materials. 

The interaction between natural and technological disasters and the study of systemic risk 

are research fields that are receiving increasing attention in the last decade although the 

preparedness for such kind of disasters is still quite low. 

The overall objective of the project is to increase the knowledge-base needed to ensure the 

security of such critical installations against severe natural events taking into account the 

scarcity of data (fortunately these are rare events). The project would analyze major 

industrial and environmental accidents from a security perspective using foresight methods 

and scenario building techniques for a better understanding of future environmental risks. In 

particular, the effects of severe weather conditions (e.g. floods) that can produce

simultaneous failures on technological installations (e.g. nuclear power plant or chemical 

installations) will be analyzed and the major vulnerabilities of the systems identified. 

An important component of the project is the development of efficient and reliable 

computational methodologies to quantify the probability of simultaneous failure and 

consequently the risk associated to such events. 

The chemical and nuclear industries will be greatly benefited by the research outcomes of 

the proposed project which will contribute towards more reliable risk assessment and 

mitigation procedures. Designing preparedness plans for multiple and simultaneous 

accidents would prove valuable not only for addressing the consequences of natural 

disasters, but other type of disasters involving multiple accidents such as acts of terrorism. 


expertise) 


interest to work with a multi-disciplinary research group. Applicants should have a 

background in relevant fields from Engineering or Environmental Science. The student will 

join a multi-disciplinary research group in the Institute for Risk and Uncertainty. 

For further details, please send a copy of your curriculum vitae to Dr. Edoardo Patelli (email: 

edoardo.patelli@liverpool.ac.uk) --- 

Name of Project: Probabilistic modelling and analysis of offshore systems/structures 

subject to hazards in arctic conditions 

Supervisor (s): Ioannis Kougioumtzoglou (Engineering) and Edoardo Patelli (Engineering); 


Outline of Project: Offshore operators (mainly oil and gas companies) rely heavily on 

seafloor installations (e.g. pipelines) to transport hydrocarbons in the Arctic regions. In this 

regard, marine pipelines are at risk due to ice keels gouging the seabed and causing large 

soil deformations. Thus, a probabilistic analysis and design methodology is required to 

realistically quantify the risk of the pipeline being damaged by ice gouging phenomena. In 

this context, there is the need to determine an optimum (i.e. safe and economical) burial 

depth for any given location. Ultimately, a design methodology will be developed and 

implemented into a risk based framework. 


expertise) 


area of probabilistic engineering mechanics. Applicants should have a background in

Engineering (preferably Civil, Mechanical, or Naval/Marine Engineering) and/or in relevant 

fields from Mathematical Sciences and/or Physics. A combined education in these fields 

would be an advantage. 

The student will join a multi-disciplinary research group in the Institute for Risk. 





Kougioumtzoglou (email: kougioum@liverpool.ac.uk) or Dr. Edoardo Patelli (email: 

edoardo.patelli@liverpool.ac.uk).

Institute for Risk and Uncertainty 

PhD Project (Brazil – Science without borders) 

Name of Project: Stochastic Modelling and Analysis of Catastrophe (CAT) Bond Products 

Supervisor (s): Ioannis Kougioumtzoglou (Engineering) and Athanasios Pantelous (IFAM, Mathemati- 

cal Sciences); further co-supervision depending on student’s background and interest 


The proposed multi-disciplinary research project focuses on the areas of financial science, engi- 

neering and mathematics. In general, the financial stability and social sustainability at a national and 

international level are always susceptible to the influence of various natural hazards. This project will 

be a groundbreaking attempt to design catastrophe (CAT) bond products for both earthquake and 

tsunami risks affecting populous cities, or/and industrial areas. In this regard, the insurance and rein- 

surance industries have been constantly looking for alternative ways to spread the risk, especially for 

such large insured losses (e.g. Swiss Re estimates claims costs of USD 1.2 billion, net of retrocession 

and before tax for Fukushima incident, Japan 2011; see released report on the 21 st of March 2011). 

Further, the potential of the developed instruments as mechanisms for transferring hazard risks 

from insurance and re-insurance companies to investors/speculators in the global capital markets 

will also be examined. Specifically, individual objectives of the project will include: 

a) Identification and quantification of the most significant parameters which describe the natural 

hazards such as location, magnitude, maximum surface acceleration, loss frequency of damages, 

loss frequency of earthquake - related fires, loss frequency of damage due to tsunami etc. 

b) The adoption of various securitization issues and the new Solvency II regulations which are cur- 

rently being used by Swiss Re and others. 

c) The development of a stochastic model for the discount interest rate parameter (e.g. Euribor 

rate). In this manner, the potentials of stochastic mechanics tools and concepts developed from 

an engineering perspective will be exploited. It is envisaged that they will offer a unique new in- 

sight and means to address complex problems in the interface of financial and engineering appli- 

cations. Next, further analysis and development of the model will be sought to allow pricing CAT 

bonds in a non-tradable (incomplete) market framework. 

PhD Project – Dr Kougioumtzoglou & Dr Pantelous 1

For training and prototype development in this virgin field the specific case of the Fukushima nuclear 

power plant incident will be considered in detail as an application example. The insurance and rein- 

surance industries will be greatly benefited by the research outcomes of the proposed project which 

will contribute towards more reliable risk assessment and enhanced decision making procedures. 

Any special features: (e.g. equipment, collaboration, industrial links, underpinning expertise) 

The project requires a strong mathematical background and a keen interest to work in the interface 

of financial mathematics and probabilistic engineering mechanics. Applicants should have either a 

background in Engineering (preferably Civil, Mechanical, or Naval/Marine Engineering) or in relevant 

fields from Mathematical and Actuarial/Financial Sciences. A combined education in these fields 

would be an advantage. The student will join a multi-disciplinary research group in the Institute for 

Risk. 

For further details, please send a copy of your curriculum vitae to either 

Dr. Ioannis Kougioumtzoglou (email: kougioum@liverpool.ac.uk) or 

Dr. Athanasios Pantelous (email: aap@liverpool.ac.uk). 

PhD Project – Dr Kougioumtzoglou & Dr Pantelous 2



Name of Project: A Stochastic Framework for Optimal Pricing Insurance Strategies 

Supervisor (s): Athanasios Pantelous (IFAM, Mathematical Sciences) and Ioannis Kougioumtzoglou 

(Engineering); further co-supervision depending on student’s background and interest 


The proposed multi-disciplinary research project focuses on the areas of actuarial, financial 

sciences, engineering and mathematics. In general, a sustained challenge in the field of financial 

mathematics is the determination of insurance premiums in a competitive market. The complexity of 

the problem increases when the flexibility/adaptation of the company’s strategy to changes of the 

premiums offered by competitor companies becomes part of the modelling. Although several 

research efforts have been made to address the aforementioned challenge, most of the models are 

case-dependent, heuristic and extensively simplified. In this research project, a realistic versatile 

stochastic framework will be developed for determining optimal premium pricing policies. 

Specifically, 

a) realistic nonlinear models will be adopted to describe the demand and the premium policy; the 

machinery of Ito stochastic calculus will be utilized to model the market average premium as a 

nonlinear stochastic differential equation. 

b) a key element in the project will be the determination of the elapsing time before market 

average premium are predicted to return to profitability. The aforementioned objective is closely 

related to the “first-passage problem” in engineering stochastic dynamics; thus, engineering 

related concepts and developed mathematical tools will be employed to address this issue 

effectively in a multi-disciplinary manner. 

c) versatile techniques such as the Wiener path integral, extensively used in physics and engineering 

related applications, will be adopted/generalized to solve the related stochastic differential 

equations in an approximate manner circumventing computationally intensive Monte Carlo 

Simulation based methods. 

PhD Project – Dr Pantelous & Kougioumtzoglou 1

The insurance and reinsurance industries will be greatly benefited by the research outcomes of the 

proposed project which will contribute towards more reliable risk assessment and enhanced 

decision making procedures. 














Name of Project: Linearization techniques for descriptor stochastic non-linear linear systems with applica- 

tions to Non-Life Insurance and Finance Finance. 

Supervisor (s): Athanasios Pantelous (IFAM, Mathematical Sciences) and Ioannis Kougioumtzoglou 

(Engineering); further co-supervision supervision depending on student’s background and interest 


Descriptor (or Generalized or Differential Differential-Algebraic) Algebraic) linear (or nonlinear) systems appear often in 

the literature of system and control theory since several significant t applications have been modelled 

and studied systematically using such kind of systems as basic model equations. Thus, the literature 

of deterministic descriptor linear systems of regular, singular or other structural type is very rich and 

well developed. Nevertheless, limited research efforts have been made in a framework of nonlinear 

stochastic models. Recently, in actuarial science, and especially for non non-life life insuranc insurance products, the 

typical portfolio of different erent insurance products and the investigation of the pricing process can be 

modelled using the framework of linear time invariant generalized stochastic discrete discrete-time models. 

Surprisingly, according to the European Parliament legislative resolution, some types of mathemat mathemati- 

cal singularities can be found (April 22, 2009, see the amended proposal for a directive of the Eur Euro- 

pean Parliament and of the Council on the taking up and pursuit of the business of Insurance and 

Reinsurance (recast) (COM (2008) 0119C6 0119C6-0231/2007 2007/0143 (COD)). Next Next, consider the n- 

degree-of-freedom freedom nonlinear system defined aas 

where E and A denote the matrices 

( ) 

( ) ( ) ( ) ( ) 

Ex Eẋ t = Ax t + g x t , x ̇ t + w ( t 

) , 

( ) 

matrices; g x ( t) , x ( t) 

̇ is an arbitrary nonlinear 

T 

of the variables q = [ q1,..., ,..., q n ] 

and T 

T 

q̇ = [ q̇ 1,..., 

q̇ 

n] 

; and w ( t ) = [ w w1 ( t ),..., w n ( t )] is a n× 1 zero- 

mean, non-stationary ary stochastic vector process possessing an evolutionary power spectrum matrix 

( ) ( ) ( 

⎡ S w w1w t 

1w ωω , t 

1 

⎢ 

⎢ S w w2w ( t) 2w ω, t 

1 

Sw ( ω, 

t) 

= ⎢ 

⎢ 

⋮ 

⎢ 

⎣ 

S w wnw ( , t ) nw ωω , t 

1 

S Sw w 1w t 

1w ωω , t 

2 

S Sw w 2w ( , t) 

2w ω t 

2 

⋯ 

⋯ 

⋱ 

S w wd w ( , t) d w ωω , t 

d d−1 S w w1w , t ⎤ 

1w 

ωω 

, t 

⎤ 

d 

⎥ 

⋮ ⎥ 

S 

⎥ 

w ( d 1w 

ωω 

, t 

⎥ . 

) 

− d ⎥ 

S Swd w ( , t ⎥ 

wd w ωω 

, t t) 

⎥ 

d ⎦ 

PhD Project – Dr Pantelous & Kougioumtzoglou 

n× 1 vector function 

) 

1

Obviously, a special case is the White noise vector process. In this research project, we would like to 

a) Apply the statistical linearization approach (e.g. Roberts and Spanos, 2003) for response deter- 

mination and investigate further the solvability properties of the equivalent linear system. The 

solvability is related to the structure of the pencil (A, B), and elements of matrix pencil or/and 

Drazin inverse theory will be applied. 

b) Apply alternative linearization techniques available for regular type stochastic differential equa- 

tions, and compare the derived results. Elements of numerical analysis and computer program- 

ming are needed. 

c) Extend the derived results to higher order systems having different kind of noise such as: 

where w( t ) is a coloured noise. 

( ) 

( ) ( ) ( ) ( ) ( ) 

Mx ̇̇ t + Cẋ t + Dx t = g x t , ẋ t + w( t) 

d) Finally, we would like to apply the result for modelling a portfolio of Non-Life insurance products; 

also, the famous Leontief model will be considered. 

The insurance and reinsurance industries will be greatly benefited by the research outcomes of the 

proposed project which will contribute towards more reliable risk assessment and enhanced deci- 

sion making procedures.

Institute of Risk http://www.liv.ac.uk/risk-and-uncertainty PhD Project ...

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