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

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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.

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Notes

  1. See Novikov [18] and a discussion in Kabanov and Pergamenshchikov [16].

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Acknowledgements

This work was supported by the Russian Science Foundation associated grants 20-68-47030 and 20-61-47043.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université Bourgogne Franche-Comté, Besançon, France

    Yuri Kabanov

  2. Lomonosov Moscow State University, Moscow, Russia

    Yuri Kabanov

  3. Laboratoire de Mathématiques Raphaël Salem, Université de Rouen - Normandie, Rouen, France

    Sergey Pergamenshchikov

  4. International Laboratory SSP&QF, National Research Tomsk State University, Tomsk, Russia

    Sergey Pergamenshchikov

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  1. Yuri Kabanov
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  2. Sergey Pergamenshchikov
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Correspondence to Yuri Kabanov.

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Kabanov, Y., Pergamenshchikov, S. On ruin probabilities with investments in a risky asset with a regime-switching price. Finance Stoch 26, 877–897 (2022). https://doi.org/10.1007/s00780-022-00483-w

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