Ruin Probability In Generalized Risk Models

The risk theory is the important branch of applied mathematics,which is used in insurance,finance,investment of securities and the management of risk. The risk theory recur to probability theory and random process theory to estabilish mathematics model, which is used to describe different kinds of risk processes. Now, the risk theory has become the important branch of acturial science,which has a very important effect in insurance theory and practice .The rearch of ruin probability not only give suggestions to the decision maker of insurance company, guiding their healthy development, but also has the important effect to make the finance market stable. On the basic of classical ruin theory, we make a certain amount of improvement for this model, and do the corresponding rearch of ruin probability. There are six chapters as follow:In the first chapter ,we chiefly discuss the background of the topic,motivation and some improvements in domestic and overseas .In the second chapter, we introduce the basic knowledge of risk theoryand the principium of ruin theory, and introduce two classical model (include short-term individual risk model, short-term aggregation model) and the applications in insurance.The third is on the basic of the second chapter, we generalize the classical compound Poisson risk model to a new model, and establish the double compound Poisson risk model. In which the income of premium is not a constant in unit time, it is a variable. Finally we deduce the expression of ruin probability of the double compound Poisson risk model, and get a upper bound for the ruin probability of this model.In the fourth chapter, we discuss the ruin probability of the risk process with correlsted negative risk sums, estabilishing the negative risk sums model which contain two kinds of risks, and deduce the expression of ruin probability of the model .Westudy how the dependence between the clasical impacts on the ruin probability.In the fifth, we introduce the concept of dividends on the basic of classical model. We use a probabilistic argument to obtain general expressions for the expected present value of dividend payments, and show how these expressions can be applied for certain individual claim amount distributions. We then consider the question of maximising the expected present value of dividend payments subject to a constraint on the insurer's ruin probability.The sixth chapter is the conclution.