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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

The paper focuses on a quantitative analysis of the probability of ruin in a finite time for a discrete risk process with proportional reinsurance and investment of the financial surplus. It is assumed that the total loss on a unit interval has either a light-tailed distribution – exponential distribution or a heavy-tailed distribution – Pareto distribution. The ruin probabilities for the finite-horizons 5 and 10 were determined from recurrence equations. Moreover, the upper bound of the ruin probability is given for the exponential distribution based on the Lundberg adjustment coefficient. This adjustment coefficient does not exist for the Pareto distribution, hence an asymptotic approximation is given for the ruin probability when the initial capital tends to infinity. The numerical results obtained are illustrated by tables and figures.

Suggested Citation

  • Helena Jasiulewicz & Wojciech Kordecki, 2015. "Ruin probability of a discrete-time risk process with proportional reinsurance and investment for exponential and Pareto distributions," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 25(3), pages 17-38.
    • Handle: RePEc:wut:journl:v:3:y:2015:p:17-38:id:1142
    DOI: 10.5277/ord150302
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    References listed on IDEAS

    as
    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.
    2. Dickson, David C. M. & Waters, Howard R., 1996. "Reinsurance and ruin," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 61-80, December.
    3. Helena Jasiulewicz, 2010. "Discrete-time financial surplus models for insurance companies," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 21, pages 225-255.
    4. Tang, Qihe & Tsitsiashvili, Gurami, 2003. "Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 299-325, December.
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    Cited by:

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    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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