{"title":"Performance of the Strong Stability Method in the Univariate Classical Risk Model","authors":"Safia Hocine, Zina Benouaret, Djamil A\u00a8\u0131ssani","volume":137,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":79,"pagesEnd":85,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10008940","abstract":"In this paper, we study the performance of the strong
\r\nstability method of the univariate classical risk model. We interest to
\r\nthe stability bounds established using two approaches. The first based
\r\non the strong stability method developed for a general Markov chains.
\r\nThe second approach based on the regenerative processes theory . By
\r\nadopting an algorithmic procedure, we study the performance of the
\r\nstability method in the case of exponential distribution claim amounts.
\r\nAfter presenting numerically and graphically the stability bounds, an
\r\ninterpretation and comparison of the results have been done.","references":"[1] D. Assani and N. V. Kartashov: Ergodicity and stability of Markov chains\r\nwith respect to operator topology in the space of transition kernels.\r\nCompte Rendu Academy of Sciences U. S. S. R (1983), 3-5.\r\n[2] Asmussen S, Ruin probabilities, World scientific, Singapore, 2000.\r\n[3] S. Asmussen and H. Albrecher, Ruin probabilities, World Scientific,\r\nSecond Ed., New Jersey, 2010.\r\n[4] J. Beirlant and S. T. Rachev, The problems of stability in insurance\r\nmathematics, Insurance: Mathematics and Economics 6, 179\u2013188, 1987.\r\n[5] D. Dickson, Insurance risk and ruin, Cambridge University Press,\r\nCambridge, 2005.\r\n[6] F. Enikeeva, V. Kalashnikov and D. Rusaityte, Continuity estimates for\r\nruin probabilities, Scandinavian Actuarial Journal, Vol. 10, 18\u201339, 2001.\r\n[7] J. Grandell, Aspect of Risk Theory, Springer-Verlage.\r\n[8] V. Kalashnikov, Topics on regenerative process, CRC Press, Boca Raton,\r\n1994. Working Paper Nr 141, March 1997.\r\n[9] V. Kalashnikov, The Stability concept for stochastic risk models,\r\nLaboratory of Actuariat Mathematics, Univarsity of Copenhagen,\r\nWorking Paper Nr 166, 2000.\r\n[10] N. V. Kartashov, Strong Stable Markov Chains, VSP, Utrecht, 1996.\r\n[11] T. Rolski, H. Schmidli, V. Schmidt and J. L. Teugels, Stochastic\r\nprocesses for insurance and finance. Wiley, New York, 1999.\r\n[12] G. E. Willmot and X. S. Lin, Lundberg approximations for compound\r\ndistributions, with insurance applications, Springer-Verlag, New York,\r\n2001.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 137, 2018"}