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On the Design of Catastrophic Risk Portfolios

Author

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  • Y.M. Ermoliev
  • T.Y. Ermolieva
  • G.J. MacDonald
  • V.I. Norkin

Abstract

Catastrophes produce rare and highly correlated insurance claims, which depend on the amount of coverage at different locations. A joint probability distribution of these claims is analytically intractable. The most promising approach for estimating total claims for a particular combination of decision variables involves geographically explicit simulations of catastrophes. The straightforward use of catastrophe models runs quickly into infinite "if - then" evaluations. The aim of this paper is to develop a framework allowing for the use of Monte Carlo simulation of catastrophes to aid decision making on designing optimal catastrophic risk portfolios. A dynamic optimization model is discussed. Connections between ruin probability and nonsmooth, in particular concave, risk functions are established. Nonsmooth adaptive Monte Carlo optimization is proposed.

Suggested Citation

  • 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.
    • Handle: RePEc:wop:iasawp:ir98056
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    References listed on IDEAS

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    1. 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.
    2. Messner, S. & Golodnikov, A. & Gritsevskii, A., 1996. "A stochastic version of the dynamic linear programming model MESSAGE III," Energy, Elsevier, vol. 21(9), pages 775-784.
    3. 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.
    4. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    5. 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.
    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.
    7. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
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    Cited by:

    1. 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.
    2. 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.

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