Some Studies On Dependent Risk Model

Insurance and actuarial mathematics is an important branch of applied mathematics , and it has the broad prospect along with the insurance business high speed development, which causes more and more many scholars to be engaged in this domain for the research work. The risk theory takes as the primary coverage of insurance mathematics, which is a current research important direction. This article mainly studied the ruin problem of dependent risks. The second chapter, ruin problems for a correlated risk model with positive risk sums,negative risk sums and positive-negative risk sums are considered. Under different premium calculation principle, the monotonicity of premium and lundberg exponent follows correlation factor in three different models is comparatively discussed respectively. and the impact on the ruin probability from the dependence between the two classes is investigated. Finally we give three examples with claim sizes being exponenti-nally distributed to show the numerical results. The third chapter, We consider a model with a dependent setting where the time between two claim occurrences determines the distribution of the nest claim size with constant interest. For the exponentially distributed claim sizes, We derive the exact analytical expressions for the Laplace transform of the ruin function . For the general claim sizes, the upper bound of the ruin probability is obtained by martingale method.