Premiums And Claims Related To Bankruptcy Probability

Much of the research work has been done in recent years on approximations and bounds of the ruin probabilities as well as the related quantities which are of interest in insurance and other areas of application in applied probability.The sum of random variables plays an important role in the research of the ruin probabilities. But, in actuarial science,the classical models are usually based on the independency assumption, that is, the random variables are assumed to be independent and identically distributed(iid). In this paper, the dependent insurance business is considered. We assume that the vector process of premiums and claims follows an first order autoregressive model . According to the time of payments, we study ruin probabilities in two generalized risk models and a constant rate is also included. Two type of different Generalized Lundberg inequalities for the ruin probabilities are derived by using martingale inequalities and a renewal recursive technique. Non-exponential upper bounds are also obtained for the ruin probabilities in this article.In the last chapter of this article, some of the numerical examples are given to show the usefulness of the upper bounds obtained in this paper and relationship between the parameters in the model and the ruin probabilities.