Upper Bounds For Ruin Probabilities In The Risk Model With A Binary Variable Interest

Ruin probabilities of the insurance risk model has been extensively studied. Riskmodel with interest is a stochastic processes for income and claim sizes of insurance com-pany, it has theoretical guidance signifcance to insurance production design and insurancemanagement. Because of the variation of market interest rates is related to time, compar-ing with the risk model with constant interest rates, it is more realistic to consider riskmodel with variable interest rates.In this paper, we consider the Sparre Andersen model modifed by the inclusion ofa binary variable interest force δt,αand θt,α, respectively. The properties of present andaccumulated surplus process are studied, and improve the adjustment coefcient equationto the equation system. In decreasing interest environment, Lundberg-type upper boundsfor the ultimate ruin probabilities are derived by martingale; More precise upper boundsfor the ultimate ruin probabilities are also given for the special case of compound Poissonmodel; Numerical comparisons of upper bounds by Monte Carlo integration are presentedfor the special case of exponential claim size in chapter3. In increasing interest environ-ment, Lundberg-type upper bounds for the ultimate ruin probabilities are also derived byrecursive techniques.