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Dependent Risks and Ruin Probabilities in Insurance

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  • H. Albrecher

Abstract

Classical risk process models in insurance rely on independency. However, especially when modeling natural events, this assumption is very restrictive. This paper proposes a new approach to introducing dependency structures between events into the model and investigates its effects on a crucial parameter for insurance companies, the probability of ruin. Explicit formulas, numerical simulations and sensitivity results for dependence are established for different dependency models of first-order markovian type indicating that for various scenarios dependency considerably increases the probability of ruin.

Suggested Citation

  • H. Albrecher, 1998. "Dependent Risks and Ruin Probabilities in Insurance," Working Papers ir98072, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:ir98072
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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. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
    3. 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.
    4. Reinhard, Jean-Marie, 1984. "On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 23-43, April.
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    Cited by:

    1. Albrecher Hansjörg & Kantor Josef, 2002. "Simulation of ruin probabilities for risk processes of Markovian type," Monte Carlo Methods and Applications, De Gruyter, vol. 8(2), pages 111-128, December.
    2. P. Nowak, 1999. "Analysis of Applications of Some Ex-Ante Instruments for the Transfer of Catastrophic Risks," Working Papers ir99075, International Institute for Applied Systems Analysis.
    3. Céline Charvériat, 2000. "Desastres naturales en América Latina y el Caribe: panorámica general del riesgo," Research Department Publications 4234, Inter-American Development Bank, Research Department.
    4. Charvériat, Céline, 2000. "Natural Disasters in Latin America and the Caribbean: An Overview of Risk," IDB Publications (Working Papers) 1804, Inter-American Development Bank.
    5. Zhengyan Lin & Xinmei Shen, 2013. "Approximation of the Tail Probability of Dependent Random Sums Under Consistent Variation and Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 165-186, March.
    6. Céline Charvériat, 2000. "Natural Disasters in Latin America and the Caribbean: An Overview of Risk," Research Department Publications 4233, Inter-American Development Bank, Research Department.

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