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

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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. 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 Pantelous & Kougioumtzoglou 2
Institute for Risk and Uncertainty PhD Project (Brazil – Science without borders) Name of Project: Linearization techniques for descriptor stochastic non-linear linear systems with applications 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 Outline of Project: 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 mathematical 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
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Institute of Risk http://www.liv.ac.uk/risk-and-uncertainty PhD Project ...

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