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Adaptive control strategies and dependence of finite time ruin on the premium loading

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  • Malinovskii, Vsevolod K.

Abstract

The paper is devoted to risk theory insight into the problem of asset-liability and solvency adaptive management. Two adaptive control strategies in the multiperiodic insurance risk model composed of chained classical risk models are introduced and their performance in terms of probability of ruin is examined. The analysis is based on an explicit expression of the probability of ruin within finite time in terms of Bessel functions. The dependence of that probability on the premium loading, either positive or negative, is a basic technical result of independent interest.

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  • Malinovskii, Vsevolod K., 2008. "Adaptive control strategies and dependence of finite time ruin on the premium loading," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 81-94, February.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:81-94
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    References listed on IDEAS

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    1. Malinovskii, Vsevolod K., 1998. "Non-Poissonian claims' arrivals and calculation of the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 123-138, June.
    2. Gerber, Hans U. & Shiu, Elias S. W., 1997. "The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 129-137, November.
    3. Drekic, Steve & Willmot, Gordon E., 2003. "On the Density and Moments of the Time of Ruin with Exponential Claims," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 11-21, May.
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    1. Malinovskii, Vsevolod K., 2014. "Improved asymptotic upper bounds on the ruin capital in the Lundberg model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 301-309.
    2. Malinovskii, Vsevolod K., 2013. "Level premium rates as a function of initial capital," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 370-380.
    3. Malinovskii, Vsevolod K., 2012. "Equitable solvent controls in a multi-period game model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 599-616.
    4. Malinovskii, Vsevolod K., 2014. "Annual intrinsic value of a company in a competitive insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 310-318.
    5. Malinovskii, Vsevolod K. & Kosova, Ksenia O., 2014. "Simulation analysis of ruin capital in Sparre Andersen’s model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 184-193.

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