A risk model with Markovian arrivals and tax payments is considered.When the insurer is in a profitable situation,the insurer may pay a certain proportion of the premium income as tax payments.First,the Laplace transf...A risk model with Markovian arrivals and tax payments is considered.When the insurer is in a profitable situation,the insurer may pay a certain proportion of the premium income as tax payments.First,the Laplace transform of the time to cross a certain level before ruin is discussed.Second,explicit formulas for a generalized Gerber-Shiu function are established in terms of the'original'Gerber-Shiu function without tax and the Laplace transform of the first passage time before ruin.Finally,the differential equations satisfied by the expected accumulated discounted tax payments until ruin are derived.An explicit expression for the discounted tax payments is also given.展开更多
基金Supported by the National Natural Science Foundation of China(10971230,11171179)the Natural Science Foundation of Shandong Province(ZR2010AQ015)the Tianyuan Fund for Mathematics(11126232)
文摘A risk model with Markovian arrivals and tax payments is considered.When the insurer is in a profitable situation,the insurer may pay a certain proportion of the premium income as tax payments.First,the Laplace transform of the time to cross a certain level before ruin is discussed.Second,explicit formulas for a generalized Gerber-Shiu function are established in terms of the'original'Gerber-Shiu function without tax and the Laplace transform of the first passage time before ruin.Finally,the differential equations satisfied by the expected accumulated discounted tax payments until ruin are derived.An explicit expression for the discounted tax payments is also given.