{"title":"Stability Bound of Ruin Probability in a Reduced Two-Dimensional Risk Model","authors":"Zina Benouaret, Djamil Aissani","volume":137,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":85,"pagesEnd":89,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10009078","abstract":"In this work, we introduce the qualitative and
\r\nquantitative concept of the strong stability method in the risk process
\r\nmodeling two lines of business of the same insurance company or
\r\nan insurance and re-insurance companies that divide between them
\r\nboth claims and premiums with a certain proportion. The approach
\r\nproposed is based on the identification of the ruin probability
\r\nassociate to the model considered, with a stationary distribution of a
\r\nMarkov random process called a reversed process. Our objective, after clarifying the condition and the perturbation
\r\ndomain of parameters, is to obtain the stability inequality of the ruin
\r\nprobability which is applied to estimate the approximation error of a
\r\nmodel with disturbance parameters by the considered model. In the
\r\nstability bound obtained, all constants are explicitly written.","references":"[1] D. Aissani, 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, ser. A, 11, 3-5, 1983.\r\n[2] S. Asmussen and H. Albrecher, Ruin Probabilities. Vol. 14 of Advanced\r\nSeries on Statistical Science Applied Probability, World Scientific, 2010.\r\n[3] F. Avram, Z. Palmowski and M. Pistorius A two-dimensional ruin\r\nproblem on the positive quadrant. Insurance: Mathematics and Economics\r\n42 (1), 227-234, 2008.\r\n[4] Z. Benouaret and D. Aissani, Strong stability in a two-dimensional\r\nclassical risk model with independent claims. Compte Rendu\r\nScandinavian Actuarial Journal. 2, 83-92, 2010.\r\n[5] A. Touazi, Z. Benouaret, D. Aissani and S. Adjabi, Nonparametric\r\nestimation of the claim amount in the strong stability analysis of the\r\nclassical risk model. Insurance: Mathematics and economics 74, 78-83,\r\n2017.\r\n[6] F. Enikeeva and V. Kalashnikov and D. Rusaityte, Continuity estimates\r\nfor ruin probabilities. Scandinavian Actuarial Journal, 1, 18-39, 2001. [7] V. Kalashnikov, The Stability concept for stochastic risk models. Working\r\nPaper Nr 166. Lab. of Actuarial Mathematics. University of Copenhagen,\r\n2000.\r\n[8] N. V. Kartashov, Strong Stable Markov Chains. VSP, Utrecht, 1999.\r\n[9] D. Rusaityte,Stability bounds for ruin probabilities in a Markov\r\nmodulated risk model with investments. Laboratory of Actuarial\r\nMathematics, University of Copenhagen. Working Paper Nr. 178, 2001.\r\n[10] V. Schmidt, T. Rolski, J. Teugels, and H. Schmidli, Stochastic Processes\r\nfor Insurance and Finance, Wiley, 1999.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 137, 2018"}