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Ruin Probabilities with Investments in Random Environment: Smoothness

Author

Listed:
  • Viktor Antipov

    (Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119234, Russia
    “Vega” Institute, Moscow 119234, Russia)

  • Yuri Kabanov

    (Moscow School of Economics, Lomonosov Moscow State University, Moscow 119234, Russia
    Laboratoire de Mathématiques, Université de Franche-Comté, 16 Route de Gray, 25030 Besançon, France)

Abstract

This paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing random variations in the economic and financial environments. We prove a sufficient condition on the distribution of jumps of the business process ensuring the smoothness of the ruin probability as a function of the initial capital and obtain for this function an integro-differential equation.

Suggested Citation

  • Viktor Antipov & Yuri Kabanov, 2024. "Ruin Probabilities with Investments in Random Environment: Smoothness," Mathematics, MDPI, vol. 12(11), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1705-:d:1405598
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    References listed on IDEAS

    as
    1. Yuri Kabanov & Sergey Pergamenshchikov, 2022. "On ruin probabilities with investments in a risky asset with a regime-switching price," Finance and Stochastics, Springer, vol. 26(4), pages 877-897, October.
    2. Paulsen, Jostein, 1993. "Risk theory in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 327-361, June.
    Full references (including those not matched with items on IDEAS)

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