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The finite time ruin probability in a risk model with capital injections

Author

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  • Ciyu Nie
  • David C.M. Dickson
  • Shuanming Li

Abstract

We consider a risk model with capital injections. We show that in the Sparre Andersen framework the density of the time to ruin for the model with capital injections can be expressed in terms of the density of the time to ruin in an ordinary Sparre Andersen risk process. In the special case of Erlang inter-claim times and exponential claims, we show that there exists a readily computable formula for the density of the time to ruin. When the inter-claim time distribution is exponential, we obtain an explicit solution for the density of the time to ruin when the individual claim amount distribution is Erlang(2), and we explain techniques to find the moments of the time to ruin. In the final section, we consider the related problem of the distribution of the duration of negative surplus in the classical risk model, and we obtain explicit solutions for the (defective) density of the total duration of negative surplus for two individual claim amount distributions.

Suggested Citation

  • Ciyu Nie & David C.M. Dickson & Shuanming Li, 2015. "The finite time ruin probability in a risk model with capital injections," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2015(4), pages 301-318, May.
    • Handle: RePEc:taf:sactxx:v:2015:y:2015:i:4:p:301-318
    DOI: 10.1080/03461238.2013.823460
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    Cited by:

    1. Teng, Ye & Zhang, Zhimin, 2023. "Finite-time expected present value of operating costs until ruin in a Cox risk model with periodic observation," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    2. Teng, Ye & Zhang, Zhimin, 2023. "On a time-changed Lévy risk model with capital injections and periodic observation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 290-314.
    3. Abouzar Bazyari, 2023. "On the Ruin Probabilities in a Discrete Time Insurance Risk Process with Capital Injections and Reinsurance," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1623-1650, August.

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