1. Why using a stochastic model

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Could the extreme risk be quantified analytically (i.e. using a formula) YES, but only in very special and simple cases or through approximations CAT + + + Reinsurance Property Attr. Property LL • Impossible to analytically express results (using a simple formula) in cases of – Reinsurance (nonproportional, surplus treaty) – Heterogeneous/correlated portfolios • Stochastic simulation (also called Monte Carlo simulation) resolves the problem – Splits generation of losses into pieces each described by analytic distributions – Applies calculations on each and every loss – Records results 7
Stochastic modeling when we are not able to calculate the distribution function • Estimate the distribution functions of some components in isolation • Simulate for these components a high number of scenarios • Combine the results on all these components for each scenario together taking into account the correlations, inflation indexes, aggregation, heterogenic business lines, non-proportional reinsurance, ... • Create the distribution functions of the variables we want to follow • Interpretation of the results To make the stochastic model, we need to make actuarial choices 8
Page 1 and 2: Using Stochastic model for choosing
Page 3 and 4: Principle of insurance is to reduce
Page 5 and 6: Recoveries Premium received Paid lo
Page 7: Approximation of the distribution f
Page 11 and 12: ReMetrica DFA Simulation MEAN = $30
Page 13 and 14: ReMetrica DFA Simulation MEAN = $30
Page 15 and 16: Our Example to be modelled • Port
Page 17 and 18: What is a surplus • The proportio
Page 19 and 20: Windstorm • Typical features: - L
Page 21 and 22: Flood • Typical feature - Flood p
Page 23 and 24: Hazard Example Digital terrain mode
Page 25 and 26: loss Output from Natural Catastroph
Page 27 and 28: Other method: Exposure rating that
Page 29 and 30: Using the software ReMetrica, used
Page 31 and 32: Measure for profitability • Avera
Page 33 and 34: What is a good risk measure • A r
Page 35 and 36: VAR Value At Risk • Only uses one
Page 37 and 38: loss Do not think that the choice o
Page 39 and 40: Outline of the presentation 1. Why
Page 41 and 42: Introducing the concept of Ceded RO
Page 43 and 44: Creation of value • Shareholders
Page 45 and 46: Conclusion Stochastic modeling is a

1. Why using a stochastic model

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