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The Design of Optimal Insurance Decisions in the Presence of Catastrophic Risks

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  • T.Y. Ermolieva

Abstract

This paper deals with the development of decision making tools for managing catastrophic (low probability - high consequences) risks. Catastrophes produce rare and highly correlated claims, which depend on various decision variables, i.e., coverages at different locations, mitigation measures and reinsurance agreements. Joint probability distributions of these claims depicting their complex spatial and temporal interactions and effects of decision variables are analytically intractable. Spatial stochastic models of catastrophes can bypass these difficulties. Catastrophic models combine the simulation of realistic and geographically explicit catastrophic events with the differentiation of property values and insurance coverages in different locations of the region. Catastrophic models can be combined with stochastic optimization techniques to aid decision making on the spatial diversification of contracts, insurance premiums, reinsurance requirements, effects of mitigation measures, and the use of other financial mechanisms. The aim of this paper is to extend a two-stage spatial catastrophic model to dynamic cases reflecting dependencies of risk accumulation processes in time. This extension is important since it can be used for the analysis of decisions under changing frequencies of events and values of properties. It is also possible to incorporate catastrophes caused by the clustering in time of such events as rains and droughts due to persistence in climate. The model can be used by individual insurers, pools of insurers or regulatory authorities.

Suggested Citation

  • T.Y. Ermolieva, 1997. "The Design of Optimal Insurance Decisions in the Presence of Catastrophic Risks," Working Papers ir97068, International Institute for Applied Systems Analysis.
  • Handle: RePEc:wop:iasawp:ir97068
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    References listed on IDEAS

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    1. Ermoliev, Yuri M. & Norkin, Vladimir I., 1997. "On nonsmooth and discontinuous problems of stochastic systems optimization," European Journal of Operational Research, Elsevier, vol. 101(2), pages 230-244, September.
    2. Philip J. Cook & Daniel A. Graham, 1977. "The Demand for Insurance and Protection: The Case of Irreplaceable Commodities," The Quarterly Journal of Economics, Oxford University Press, vol. 91(1), pages 143-156.
    3. Tucker, Michael, 1997. "Climate change and the insurance industry: the cost of increased risk and the impetus for action," Ecological Economics, Elsevier, vol. 22(2), pages 85-96, August.
    4. Mayers, David & Smith, Clifford W, Jr, 1983. "The Interdependence of Individual Portfolio Decisions and the Demand for Insurance," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 304-311, April.
    5. Y.M. Ermoliev & V.I. Norkin, 1997. "Stochastic Generalized Gradient Method with Application to Insurance Risk Management," Working Papers ir97021, International Institute for Applied Systems Analysis.
    6. T.Y. Ermolieva & Y.M. Ermoliev & V.I. Norkin, 1997. "Spatial Stochastic Model for Optimization Capacity of Insurance Networks Under Dependent Catastrophic Risks: Numerical Experiments," Working Papers ir97028, International Institute for Applied Systems Analysis.
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    Cited by:

    1. Y.M. Ermoliev & T.Y. Ermolieva & G.J. MacDonald & V.I. Norkin, 1998. "On the Design of Catastrophic Risk Portfolios," Working Papers ir98056, International Institute for Applied Systems Analysis.
    2. Ermoliev, Y. & Ermolieva, T. & Fischer, G. & Makowski, M. & Nilsson, S. & Obersteiner, M., 2008. "Discounting, catastrophic risks management and vulnerability modeling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 917-924.
    3. Ermoliev, Yuri M. & Ermolieva, Tatiana Y. & MacDonald, Gordon J. & Norkin, Vladimir I. & Amendola, Aniello, 2000. "A system approach to management of catastrophic risks," European Journal of Operational Research, Elsevier, vol. 122(2), pages 452-460, April.
    4. Y.M. Ermoliev & V.I. Norkin, 1998. "Monte Carlo Optimization and Path Dependent Nonstationary Laws of Large Numbers," Working Papers ir98009, International Institute for Applied Systems Analysis.
    5. L.A. Korf, 1998. "Insurer's Portfolios of Risks: Approximating Infinite Horizon Stochastic Dynamic Optimization Problems," Working Papers ir98061, International Institute for Applied Systems Analysis.
    6. B.V. Digas & Y.M. Ermoliev & A.V. Kryazhimskii, 1998. "Guaranteed Optimization in Insurance of Catastrophic Risks," Working Papers ir98082, International Institute for Applied Systems Analysis.
    7. H. Albrecher, 1998. "Dependent Risks and Ruin Probabilities in Insurance," Working Papers ir98072, International Institute for Applied Systems Analysis.

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