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Probabilistic approach to risk processes with level-dependent premium rate

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  • Denisov, Denis
  • Gotthardt, Niklas
  • Korshunov, Dmitry
  • Wachtel, Vitali

Abstract

We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin probability; our proving technique is purely probabilistic and based on the analysis of Markov chains with asymptotically zero drift.

Suggested Citation

  • Denisov, Denis & Gotthardt, Niklas & Korshunov, Dmitry & Wachtel, Vitali, 2024. "Probabilistic approach to risk processes with level-dependent premium rate," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 142-156.
    • Handle: RePEc:eee:insuma:v:118:y:2024:i:c:p:142-156
    DOI: 10.1016/j.insmatheco.2024.06.002
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    References listed on IDEAS

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    1. Czarna, Irmina & Pérez, José-Luis & Rolski, Tomasz & Yamazaki, Kazutoshi, 2019. "Fluctuation theory for level-dependent Lévy risk processes," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5406-5449.
    2. Ewa Marciniak & Zbigniew Palmowski, 2016. "On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums," Papers 1604.06892, arXiv.org.
    3. Denisov, Denis & Korshunov, Dmitry & Wachtel, Vitali, 2013. "Potential analysis for positive recurrent Markov chains with asymptotically zero drift: Power-type asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3027-3051.
    4. Ewa Marciniak & Zbigniew Palmowski, 2016. "On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 723-742, February.
    5. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
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