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Stochastic Optimization of Insurance Portfolios for Managing Exposure to Catastrophic Risks

Author

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

Abstract

A catastrophe may affect different locations and produce losses that are rare and highly correlated in space and time. It may ruin many insurers if their risk exposures are not properly diversified among locations. The multidimentional distribution of claims from different locations depends on decision variables such as the insurer's coverage at different locations, on spatial and temporal characteristics of possible catastrophes and the vulnerability of insured values. As this distribution is analytically intractable, the most promising approach for managing the exposure of insurance portfolios to catastrophic risks requires geographically explicit simulations of catastrophes. The straightforward use of so-called catastrophe modeling runs quickly into an extremely large number of “what-if” evaluations. The aim of this paper is to develop an approach that integrates catastrophe modeling with stochastic optimization techniques to support decision making on coverages of losses, profits, stability, and survival of insurers. We establish connections between ruin probability and the maximization of concave risk functions and we outline numerical experiments. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Y.M. Ermoliev & T.Y. Ermolieva & G.J. MacDonald & V.I. Norkin, 2000. "Stochastic Optimization of Insurance Portfolios for Managing Exposure to Catastrophic Risks," Annals of Operations Research, Springer, vol. 99(1), pages 207-225, December.
    • Handle: RePEc:spr:annopr:v:99:y:2000:i:1:p:207-225:10.1023/a:1019244405392
    DOI: 10.1023/A:1019244405392
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    Cited by:

    1. 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.
    2. Ermolieva, Tatiana, 2005. "Simulation-based optimization of social security systems under uncertainty," European Journal of Operational Research, Elsevier, vol. 166(3), pages 782-793, November.
    3. Martin Branda & Jitka Dupačová, 2012. "Approximation and contamination bounds for probabilistic programs," Annals of Operations Research, Springer, vol. 193(1), pages 3-19, March.
    4. I. Bremer & R. Henrion & A. Möller, 2015. "Probabilistic constraints via SQP solver: application to a renewable energy management problem," Computational Management Science, Springer, vol. 12(3), pages 435-459, July.
    5. Tatiana Ermolieva & Petr Havlík & Yuri Ermoliev & Aline Mosnier & Michael Obersteiner & David Leclère & Nikolay Khabarov & Hugo Valin & Wolf Reuter, 2016. "Integrated Management of Land Use Systems under Systemic Risks and Security Targets: A Stochastic Global Biosphere Management Model," Journal of Agricultural Economics, Wiley Blackwell, vol. 67(3), pages 584-601, September.
    6. Yuri Ermoliev & Tatiana Ermolieva & Guenther Fischer & Marek Makowski, 2010. "Extreme events, discounting and stochastic optimization," Annals of Operations Research, Springer, vol. 177(1), pages 9-19, June.
    7. Tatiana Ermolieva & Yuri Ermoliev & Guenther Fischer & Istvan Galambos, 2003. "The Role of Financial Instruments in Integrated Catastrophic Flood Management," Multinational Finance Journal, Multinational Finance Journal, vol. 7(3-4), pages 207-230, September.
    8. Emilio L. Cano & Javier M. Moguerza & Tatiana Ermolieva & Yurii Yermoliev, 2017. "A strategic decision support system framework for energy-efficient technology investments," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 249-270, July.
    9. T. Ermolieva & T. Filatova & Y. Ermoliev & M. Obersteiner & K. M. de Bruijn & A. Jeuken, 2017. "Flood Catastrophe Model for Designing Optimal Flood Insurance Program: Estimating Location‐Specific Premiums in the Netherlands," Risk Analysis, John Wiley & Sons, vol. 37(1), pages 82-98, January.
    10. Martin Branda, 2013. "On relations between chance constrained and penalty function problems under discrete distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 265-277, April.
    11. Tatiana Ermolieva & Petr Havlik & Yuri Ermoliev & Nikolay Khabarov & Michael Obersteiner, 2021. "Robust Management of Systemic Risks and Food-Water-Energy-Environmental Security: Two-Stage Strategic-Adaptive GLOBIOM Model," Sustainability, MDPI, vol. 13(2), pages 1-16, January.

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