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2015 | 25 | nr 3 | 17--38
Tytuł artykułu

Ruin Probability of a Discrete-Time Risk Process with Proportional Reinsurance and Investment for the Exponential and Pareto Distributions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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. (original abstract)
Rocznik
Tom
25
Numer
Strony
17--38
Opis fizyczny
Twórcy
  • Wrocław University of Environmental and Life Sciences, Poland
  • Witelon State University of Applied Sciences in Legnica
Bibliografia
  • [1] CAI J., Discrete time risk models under rates of interest, Prob. Eng. Inf. Sci., 2002, 16, 309.
  • [2] CAI J., Ruin probabilities with dependent rates of interest, J. Appl. Prob., 2002, 39, 312.
  • [3] CAI J., DICKSON D.C.M., Ruin probabilities with a Markov chain interest model, Insurance Math. Econom., 2004, 35, 513.
  • [4] DIASPARRA M.A., ROMERA R., Bounds for the ruin probability of a discrete-time risk process, J. Appl. Probab., 2009, 46, 99.
  • [5] DICKSON D.C.M., WATERS H.R., Reinsurance and ruin. Insurance, Math. Econom., 1996, 19, 61.
  • [6] JASIULEWICZ H., Discrete-time financial surplus models for insurance companies, Ann. Coll. Econ. Anal., 2010, 21, 225.
  • [7] JASIULEWICZ H., Discrete risk process with reinsurance and random interest rate, Ann. Coll. Econ. Anal., 2013, 31, 11 (in Polish).
  • [8] PALMOWSKI Z., Approximations of ruin probability of insurance company in diffusion Cox model, Res. Pap. Wrocław Univ Econ., 2006, 1108, 34 (in Polish).
  • [9] 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.
  • [10] YANG H., Non-exponential bounds for ruin probability with interest effect included, Scand. Act. J., 1999, 99, 66.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ekon-element-000171403421

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