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Elementary Bounds on the Ruin Capital in a Diffusion Model of Risk

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  • Vsevolod K. Malinovskii

    (Central Economics and Mathematics Institute (CEMI) of Russian Academy of Science, Nakhimovskiy prosp., 47, Moscow 117418, Russia)

Abstract

In a diffusion model of risk, we focus on the initial capital needed to make the probability of ruin within finite time equal to a prescribed value. It is defined as a solution of a nonlinear equation. The endeavor to write down and to investigate analytically this solution as a function of the premium rate seems not technically feasible. Instead, we obtain informative bounds for this capital in terms of elementary functions.

Suggested Citation

  • Vsevolod K. Malinovskii, 2014. "Elementary Bounds on the Ruin Capital in a Diffusion Model of Risk," Risks, MDPI, vol. 2(3), pages 1-11, July.
    • Handle: RePEc:gam:jrisks:v:2:y:2014:i:3:p:249-259:d:37899
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    References listed on IDEAS

    as
    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, 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.
    3. Malinovskii, Vsevolod K., 2013. "Level premium rates as a function of initial capital," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 370-380.
    4. 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.
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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.

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