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On ruin probabilities with investments in a risky asset with a regime-switching price

Author

Listed:
  • Yuri Kabanov

    (Université Bourgogne Franche-Comté
    Lomonosov Moscow State University)

  • Sergey Pergamenshchikov

    (Université de Rouen - Normandie
    National Research Tomsk State University)

Abstract

We investigate the asymptotics of ruin probabilities when the company invests its reserve in a risky asset with a regime-switching price. We assume that the asset price is a conditional geometric Brownian motion with parameters modulated by a Markov process with a finite number of states. Using techniques from implicit renewal theory, we obtain the rate of convergence to zero of the ruin probabilities as the initial capital tends to infinity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:4:d:10.1007_s00780-022-00483-w
    DOI: 10.1007/s00780-022-00483-w
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    References listed on IDEAS

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    1. Hansjörg Albrecher & Hans Gerber & Hailiang Yang, 2010. "A Direct Approach to the Discounted Penalty Function," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(4), pages 420-434.
    2. Pergamenshchikov, Serguei & Zeitouny, Omar, 2006. "Ruin probability in the presence of risky investments," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 267-278, February.
    3. Behme, Anita & Lindner, Alexander & Reker, Jana & Rivero, Victor, 2021. "Continuity properties and the support of killed exponential functionals," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 115-146.
    4. Buraczewski, Dariusz & Damek, Ewa, 2017. "A simple proof of heavy tail estimates for affine type Lipschitz recursions," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 657-668.
    5. 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.
    6. 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.
    7. Paulsen, Jostein, 1993. "Risk theory in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 327-361, June.
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    Cited by:

    1. Viktor Antipov & Yuri Kabanov, 2024. "Ruin Probabilities with Investments in Random Environment: Smoothness," Mathematics, MDPI, vol. 12(11), pages 1-12, May.

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    More about this item

    Keywords

    Ruin probabilities; Risky investments; Stochastic volatility; Hidden Markov model; Regime switching; Implicit renewal theory;
    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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