The Analysis Of The Duration Of The Negative Surplus For A Generalized Compounded Poisson-geometric Risk Model

In this paper,we focus on the duration of the negative surplus(DNS) under a generalized compounded Poisson-Geometric risk model. On the one hand,by taking full advantage of the strong Markov property of the surplus process and the total expectation formula,we derive the distribution of the deficit at ruin; On the other hand,we use a new method differents with the Gerber(1990)'s martin-gale method,by using a new stopping time,we get the differential equation of the random variable and the moment generating functions of the DNS.