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Ruin probability of a discrete-time risk process with proportional reinsurance and investment for exponential and Pareto distributions

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  • Helena Jasiulewicz
  • Wojciech Kordecki

Abstract

In this paper a quantitative analysis of the ruin probability in finite time of discrete risk process with proportional reinsurance and investment of finance surplus is focused on. It is assumed that the total loss on a unit interval has a light-tailed distribution -- exponential distribution and a heavy-tailed distribution -- Pareto distribution. The ruin probability for finite-horizon 5 and 10 was determined from recurrence equations. Moreover for exponential distribution the upper bound of ruin probability by Lundberg adjustment coefficient is given. For Pareto distribution the adjustment coefficient does not exist, hence an asymptotic approximation of the ruin probability if an initial capital tends to infinity is given. Obtained numerical results are given as tables and they are illustrated as graphs.

Suggested Citation

  • Helena Jasiulewicz & Wojciech Kordecki, 2013. "Ruin probability of a discrete-time risk process with proportional reinsurance and investment for exponential and Pareto distributions," Papers 1306.3479, arXiv.org, revised Mar 2015.
    • Handle: RePEc:arx:papers:1306.3479
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    References listed on IDEAS

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    1. Cai, Jun & Dickson, David C.M., 2004. "Ruin probabilities with a Markov chain interest model," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 513-525, December.
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    Cited by:

    1. Ernesto Cruz & Luis Rincón & David J. Santana, 2024. "Ruin Probabilities as Recurrence Sequences in a Discrete-Time Risk Process," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-16, September.
    2. Ekaterina Bulinskaya & Boris Shigida, 2021. "Discrete-Time Model of Company Capital Dynamics with Investment of a Certain Part of Surplus in a Non-Risky Asset for a Fixed Period," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 103-121, March.

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