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The ruin problem of the renewal ri model with stochastic income

Xiang Ming-yin, Sun Jing-yun, Tian Li-na

In this paper, we consider the renewal risk model with stochastic income. In which, the premium process is modelled by a compound Poisson process and claim inter-arrival times are generalized Erlang (2) distributed. A system of integral equations for the discounted penalty function is derived. In the case of both premium and claim are exponential distributed closed form expression for Laplace transform of ruin probability is obtained, and a numerical answer of ruin probability as a example is given.