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

• Authors: Helena JASIULEWICZ , Wojciech KORDECKI
• Languages of publication: EN

Abstracts

EN

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 heavytailed 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.

Keywords

EN

discrete time risk process; ruin probability, proportional reinsurance Lundberg’s inequality; regularly varying tail

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2015
• Volume: 25
• Issue: 3
• Pages: 17-38

Contributors

author

Helena JASIULEWICZ

• Wrocław University of Environmental and Life Sciences, Institute of Economics and Social Sciences, ul. Norwida 25, 50-375 Wrocław, Poland

author

Wojciech KORDECKI

• The Witelon State University of Applied Sciences in Legnica, Faculty of Technical and Economic Science, 59-220 Legnica, ul. Sejmowa 5C, Poland

References

• CAI J., Discrete time risk models under rates of interest, Prob. Eng. Inf. Sci., 2002, 16, 309.
• CAI J., Ruin probabilities with dependent rates of interest, J. Appl. Prob., 2002, 39, 312.
• CAI J., DICKSON D.C.M., Ruin probabilities with a Markov chain interest model, Insurance Math. Econom., 2004, 35, 513.
• DIASPARRA M.A., ROMERA R., Bounds for the ruin probability of a discrete-time risk process, J. Appl. Probab., 2009, 46, 99.
• DICKSON D.C.M., WATERS H.R., Reinsurance and ruin. Insurance, Math. Econom., 1996, 19, 61.
• JASIULEWICZ H., Discrete-time financial surplus models for insurance companies, Ann. Coll. Econ. Anal., 2010, 21, 225.
• JASIULEWICZ H., Discrete risk process with reinsurance and random interest rate, Ann. Coll. Econ. Anal., 2013, 31, 11 (in Polish).
• PALMOWSKI Z., Approximations of ruin probability of insurance company in diffusion Cox model, Res. Pap. Wrocław Univ Econ., 2006, 1108, 34 (in Polish).
• TANG Q., TSITSIASHVILI G., Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risk, Stoch. Proc. Appl., 2003, 108, 299.
• YANG H., Non-exponential bounds for ruin probability with interest effect included, Scand. Act. J., 1999, 99, 66.

Identifiers

DOI

10.5277/ord150302