جستجوی مقالات مرتبط با کلیدواژه « infinite time ruin probability » در نشریات گروه « آمار »

In risk models, the ruin probabilities and ‎Lundberg‎ bound are calculated despite knowing the statistical distribution of random variables. In the present paper, for collective risk model and discrete time risk model of insurance company for independent and identically distributed claims with light-tailed distribution, the infinite time ruin probabilities are computed using Lundberg bound, moreover the general forms of density functions of random variables of claim sizes are derived. ‎‎‎For some special cases in the discrete time risk model, the density functions of claim sizes have the shifted geometric distribution, and for the collective risk model, they always have an exponential distribution.‎ ‎ ‎‎Presenting the numerical examples of infinite time ruin probabilities and the simulated values of these probabilities and the Lundberg bound are the final results of this article.

In this paper, the individual risk model of the insurance company with dependent claims is considered and assumes that the binary vector of random variables of claim sizes is independent. Also, they have a common joint distribution function. A recursive formula for infinite time ruin probability is obtained according to the initial reserve and joint probability density function of random variables of claim sizes using probability inequalities and the induction method. Some numerical examples and simulation studies are presented for checking the results related to the light-tailed bivariate Poisson, heavy-tailed Log-Normal and Pareto distributions. The results are compared for Farlie–Gambel–Morgenstern and bivariate Frank copula functions. The effect of claims with heavy-tailed distributions on the ruin probability is also investigated.