International Science Index


10008940

Performance of the Strong Stability Method in the Univariate Classical Risk Model

Abstract:In this paper, we study the performance of the strong stability method of the univariate classical risk model. We interest to the stability bounds established using two approaches. The first based on the strong stability method developed for a general Markov chains. The second approach based on the regenerative processes theory . By adopting an algorithmic procedure, we study the performance of the stability method in the case of exponential distribution claim amounts. After presenting numerically and graphically the stability bounds, an interpretation and comparison of the results have been done.
References:
[1] D. Assani and N. V. Kartashov: Ergodicity and stability of Markov chains with respect to operator topology in the space of transition kernels. Compte Rendu Academy of Sciences U. S. S. R (1983), 3-5.
[2] Asmussen S, Ruin probabilities, World scientific, Singapore, 2000.
[3] S. Asmussen and H. Albrecher, Ruin probabilities, World Scientific, Second Ed., New Jersey, 2010.
[4] J. Beirlant and S. T. Rachev, The problems of stability in insurance mathematics, Insurance: Mathematics and Economics 6, 179–188, 1987.
[5] D. Dickson, Insurance risk and ruin, Cambridge University Press, Cambridge, 2005.
[6] F. Enikeeva, V. Kalashnikov and D. Rusaityte, Continuity estimates for ruin probabilities, Scandinavian Actuarial Journal, Vol. 10, 18–39, 2001.
[7] J. Grandell, Aspect of Risk Theory, Springer-Verlage.
[8] V. Kalashnikov, Topics on regenerative process, CRC Press, Boca Raton, 1994. Working Paper Nr 141, March 1997.
[9] V. Kalashnikov, The Stability concept for stochastic risk models, Laboratory of Actuariat Mathematics, Univarsity of Copenhagen, Working Paper Nr 166, 2000.
[10] N. V. Kartashov, Strong Stable Markov Chains, VSP, Utrecht, 1996.
[11] T. Rolski, H. Schmidli, V. Schmidt and J. L. Teugels, Stochastic processes for insurance and finance. Wiley, New York, 1999.
[12] G. E. Willmot and X. S. Lin, Lundberg approximations for compound distributions, with insurance applications, Springer-Verlag, New York, 2001.