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Equitable solvent controls in a multi-period game model of risk

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  • Malinovskii, Vsevolod K.

Abstract

In insurance two major types of cycles are known: (a) regular many years long up- and down-swings referred to as underwriting cycles and (b) irregular short-range fluctuations. The key rationale of the underwriting cycles is migration of insureds triggered by the insurers’ price competition while the short-range fluctuations are due to unpredictable fluctuations in economic surroundings. The competition-originated cycles were modeled in the framework of a Lundberg’s-type multi-period model of risk in Malinovskii (2010, submitted for publication). Short-range fluctuations were modeled under diverse nature scenarios in the framework of (i) diffusion (see Malinovskii, 2007, 2009) and (ii) Lundberg’s-type multi-period model (see Malinovskii, 2008a). In this paper the results of Malinovskii (2009) are extended on the Lundberg’s-type multi-period model.

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  • 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.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:3:p:599-616
    DOI: 10.1016/j.insmatheco.2012.08.001
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    References listed on IDEAS

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    1. Malinovskii, V. K., 2007. "Zone-Adaptive Control Strategy for a Multiperiodic Model of Risk," Annals of Actuarial Science, Cambridge University Press, vol. 2(2), pages 349-367, September.
    2. 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.
    3. Malinovskii, Vsevolod K., 2010. "Competition-Originated Cycles and Insurance Strategies," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 797-843, November.
    4. De Vylder, F. Etienne & Goovaerts, Marc J., 1999. "Explicit finite-time and infinite-time ruin probabilities in the continuous case," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 155-172, May.
    5. Malinovskii, Vsevolod K., 2009. "Scenario Analysis for a Multi-Period Diffusion Model of Risk," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 649-676, November.
    6. 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.
    7. Rongming, Wang & Haifeng, Liu, 2002. "On the Ruin Probability Under a Class of Risk Processes1," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 81-90, May.
    8. Malinovskii, Vsevolod K., 2008. "Risk theory insight into a zone-adaptive control strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 656-667, April.
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    Cited by:

    1. 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.
    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. Vsevolod Malinovskii, 2020. "Value-at-Risk substitute for non-ruin capital is fallacious and redundant," Papers 2005.05428, arXiv.org.
    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., 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.
    6. Malinovskii, Vsevolod K., 2013. "Rationale of underwriters’ pricing conduct on competitive insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 325-333.

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