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Asymptotic And Numerical Solutions For Diffusion Models For Compounded Risk Reserves With Dividend Payments, Sally S. L. Shao, C. L. Chang

Mathematics and Statistics Faculty Publications

We study a family of diffusion models for compounded risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. We are interested in the models in which the dividend payments are paid from the risk reserves. After defining the process of conditional probability in finite time, martingale theory turns the nonlinear stochastic differential equation to a special class of boundary value problems defined by a parabolic equation with a nonsmooth coefficient of the convection term. Based on the behavior of the total income flow, asymptotic and numerical methods are used to solve the …