Insurability of catastrophic risks: the stochastic optimization model

Catastrophes produce losses highly correlated in space and time, which break the law of large numbers. We derive the insurability of dependent catastrophic risks by calculating conditions that would aid insurers in deliberate selection of their portfolios. This paper outlines the general structure of a basic stochastic optimization model. Connections between the probability of ruin and nonsmooth risk functions, as well as adaptive Monte Carlo optimization procedures and path dependent laws of large numbers, are discussed

[1]  András Prékopa,et al.  Numerical Solution of Probabilistic Constrained Programming Problems , 1988 .

[2]  Harrison H. Barrett,et al.  3 – Theory of Random Processes , 1981 .

[3]  O. Giarini.  The diminishing returns of technology , 1978 .

[4]  Yuri Ermoliev,et al.  On nonsmooth and discontinuous problems of stochastic systems optimization , 1997 .

[5]  Stavros A. Zenios,et al.  Designing Portfolios of Financial Products via Integrated Simulation and Optimization Models , 1999, Oper. Res..

[6]  Wlodzimierz Ogryczak,et al.  From stochastic dominance to mean-risk models: Semideviations as risk measures , 1999, Eur. J. Oper. Res..

[7]  Yuri Ermoliev,et al.  On the Design of Catastrophic Risk Portfolios , 1998 .

[8]  J. Grandell.  Aspects of Risk Theory , 1991 .

[9]  K. Marti,et al.  Approximations and Derivatives of Probability Functions , 1994 .

[10]  Yuri Ermoliev,et al.  Monte Carlo Optimization and Path Dependent Nonstationary Laws of Large Numbers , 1998 .

[11]  Kenneth J. Arrow,et al.  The theory of risk-bearing: Small and great risks , 1996 .

[12]  Harvey E. Lapan,et al.  The Mathematical Theory of Insurance. , 1975 .

[13]  Tatiana Ermolieva,et al.  The Design of Optimal Insurance Decisions in the Presence of Catastrophic Risks , 1997 .

[14]  W. Sharpe,et al.  Mean-Variance Analysis in Portfolio Choice and Capital Markets , 1987 .

[15]  J. Neveu,et al.  Mathematical foundations of the calculus of probability , 1965 .

[16]  Victor Ginsburgh,et al.  The Structure of Applied General Equilibrium Models , 1997 .

[17]  E. L. Pugh.  A Gradient Technique of Adaptive Monte Carlo , 1966 .

[18]  Vladimir I. Norkin,et al.  Generalized-differentiable functions , 1980 .

[19]  Roger J.-B. Wets.  Challenges in stochastic programming , 1996, Math. Program..

[20]  Y. Ermoliev,et al.  Stochastic Generalized Gradient Method with Application to Insurance Risk Management , 1997 .

[21]  Yuri Ermoliev,et al.  Spatial Stochastic Model for Optimization Capacity of Insurance Networks Under Dependent Catastrophic Risks: Numerical Experiments , 1997 .

[22]  A Orman,et al.  Optimization of Stochastic Models: The Interface Between Simulation and Optimization , 2012, J. Oper. Res. Soc..

[23]  George Ch. Pflug,et al.  Optimization of Stochastic Models , 1996 .