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Ruin probabilities for a Sparre Andersen model with investments: the case of annuity payments

Author

Listed:
  • Yuri Kabanov

    (Lomonosov Moscow State University
    Université de Franche-Comté)

  • Platon Promyslov

    (Lomonosov Moscow State University
    Institute “Vega”)

Abstract

This note is a complement to the paper (Stoch. Process. Appl. 144:72–84, 2022) by Eberlein, Kabanov and Schmidt on the asymptotics of the ruin probability in a Sparre Andersen non-life insurance model with investments into a risky asset whose price follows a geometric Lévy process. Using techniques from the theory of semi-Markov processes, we extend the result of (Eberlein, Kabanov and Schmidt in Stoch. Process. Appl. 144:72–84, 2022) to the case of annuities and models with two-sided jumps.

Suggested Citation

  • Yuri Kabanov & Platon Promyslov, 2023. "Ruin probabilities for a Sparre Andersen model with investments: the case of annuity payments," Finance and Stochastics, Springer, vol. 27(4), pages 887-902, October.
    • Handle: RePEc:spr:finsto:v:27:y:2023:i:4:d:10.1007_s00780-023-00513-1
    DOI: 10.1007/s00780-023-00513-1
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    References listed on IDEAS

    as
    1. Paulsen, Jostein, 1998. "Sharp conditions for certain ruin in a risk process with stochastic return on investments," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 135-148, June.
    2. Yuri Kabanov & Serguei Pergamenshchikov, 2020. "Ruin probabilities for a Lévy-driven generalised Ornstein–Uhlenbeck process," Finance and Stochastics, Springer, vol. 24(1), pages 39-69, January.
    3. Albrecher, Hansjoerg & Constantinescu, Corina & Thomann, Enrique, 2012. "Asymptotic results for renewal risk models with risky investments," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3767-3789.
    4. Eberlein, Ernst & Kabanov, Yuri & Schmidt, Thorsten, 2022. "Ruin probabilities for a Sparre Andersen model with investments," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 72-84.
    5. 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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    More about this item

    Keywords

    Ruin probabilities; Sparre Andersen model; Actuarial models with investments; Renewal processes; Annuities; Distributional equations;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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