Dividend maximization in an insurance process compounded by investment of black and scholestype

This dissertation deals with the problem of dividend maximization in an insurance process. This area of non life insurance can be traced in the works of De Finetti as far back as 1957. The main concept used is maximization using the Hamilton Jacobi Bellman equations, while using stochastic processes. First, the model has been formulated theoretically with all the parameters assumed to be unknown but from a certain set. The maximum dividends that an insurer can pay to the shareholders at any time before ruin occurs can be calculated from the HJB equation. The effect of investment on the dividends paid to share holdershas been investigated from the dividend value function. Numerical schemes to approximate the solutions have been developed in cases where exact solutions are hard to find. These schemes are first tested for cases where exact solutions exist to check their levels of accuracy. The model has been validated using common parameters in literature. The dividend payment strategy that is considered in this study is the barrier strategy. Numerical computations in this study are done using a Pentium M processor computer with a 1GB RAM. The software that has been used is mainly Maple 7, although other softwares like Matlab7 were found to give similar results. The results that are obtained in this study are shown in chapter five. The optimal barrier levels are determined for selected parameters and the corresponding value functions are also determined in such cases. The ODE method that is used shows a high level of accuracy and is recommended for use in dividend maximization problems. However, it poses a problem of having to convert the IDE into an ODE. The Homotopy Analysis Method has been found efficient to solve problems with many claims size distributions.