Numerical Algorithm for the Stochastic Present Value of Aggregate Claims in the Renewal Risk Model

For the stochastic present value of aggregate claims in the renewal risk model, a numerical algorithm is constructed based on the Monte Carlo and random process principle. The basic idea and design process of this algorithm is detailed. The numerical simulation results show that it is consistence with the theory analysis result under different parameter different distribution. The numerical algorithm results can directly see the ruin probability of this renewal risk model, to develop support in the actual decision.