Approximations of the Optimal Dividends Barrier in Classical Risk Model

We consider methods for estimating the optimal dividend barrier in the classical risk model. If an individual claim is a mixtures of exponential probability density function, we obtain a closed form expression for expectation of the discounted dividends and exact value of the optimal dividends barrier by laplace transform. When the analytic result for expectation of the discounted dividends is unavailable, two methods are provided to estimate the optimal dividends barrier, one is by the famous Cramer-lundberg asymptotic formula, the other is by discrete time model. For illustration, the approximate values of optimal dividends are compared numerically with the exact values in two numerical examples. The results show that the optimal dividends barrier can be effectively estimated by Cramer-lundberg asymptotic formula and discrete time model.