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The Reduction of Initial Reserves Using the Optimal Reinsurance Chains in Non-Life Insurance

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  • Galina Horáková

    (Department of Mathematics & Actuarial Science, Faculty of Economic Informatics, University of Economics in Bratislava, Dolnozemská Cesta 1/b, 852 35 Bratislava, Slovakia)

  • František Slaninka

    (Department of Mathematics & Actuarial Science, Faculty of Economic Informatics, University of Economics in Bratislava, Dolnozemská Cesta 1/b, 852 35 Bratislava, Slovakia)

  • Zsolt Simonka

    (Department of Mathematics & Actuarial Science, Faculty of Economic Informatics, University of Economics in Bratislava, Dolnozemská Cesta 1/b, 852 35 Bratislava, Slovakia)

Abstract

The aim of the paper is to propose, and give an example of, a strategy for managing insurance risk in continuous time to protect a portfolio of non-life insurance contracts against unwelcome surplus fluctuations. The strategy combines the characteristics of the ruin probability and the values VaR and CVaR . It also proposes an approach for reducing the required initial reserves by means of capital injections when the surplus is tending towards negative values, which, if used, would protect a portfolio of insurance contracts against unwelcome fluctuations of that surplus. The proposed approach enables the insurer to analyse the surplus by developing a number of scenarios for the progress of the surplus for a given reinsurance protection over a particular time period. It allows one to observe the differences in the reduction of risk obtained with different types of reinsurance chains. In addition, one can compare the differences with the results obtained, using optimally chosen parameters for each type of proportional reinsurance making up the reinsurance chain.

Suggested Citation

  • Galina Horáková & František Slaninka & Zsolt Simonka, 2021. "The Reduction of Initial Reserves Using the Optimal Reinsurance Chains in Non-Life Insurance," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1350-:d:573205
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    References listed on IDEAS

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    1. Dickson,David C. M., 2016. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9781107154605.
    2. Schmidli, H., 1995. "Cramer-Lundberg approximations for ruin probabilities of risk processes perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 135-149, May.
    3. Dickson, David C.M. & Waters, Howard R., 2004. "Some Optimal Dividends Problems," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 49-74, May.
    4. Hossack,I. B. & Pollard,J. H. & Zehnwirth,B., 1999. "Introductory Statistics with Applications in General Insurance," Cambridge Books, Cambridge University Press, number 9780521652346.
    5. Dickson, David C.M., 2012. "The joint distribution of the time to ruin and the number of claims until ruin in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 334-337.
    6. Hossack,I. B. & Pollard,J. H. & Zehnwirth,B., 1999. "Introductory Statistics with Applications in General Insurance," Cambridge Books, Cambridge University Press, number 9780521655347.
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