Optimal Dividend Payment Strategy under Stochastic Interest Force

Abstract

This paper attempts to study the optimal dividend barrier strategy in risk analysis of an insurance company under stochastic discount interest. Based on stochastic perturbation methodology, we first describe the random of interest by Wiener Process and Poisson process and yield some theoretical results satisfied by optimal dividend barrier. In the case of an exponential individual claim distribution, a group of barrier values are obtained. Meanwhile we also discuss the effect of stochastic interest on the barrier by data analysis and direct interpretations about interest models. It is found that the barrier is more sensitive to constant interest force than other parameters in interest model and the effect of diffusion coefficient on barrier is less sensitive than that of Poisson coefficient. These all provide insights into the effect of stochastic interest on the optimal barrier, and show the importance of introducing stochastic interest. Finally, we propose several meaningful and follow-up problems, for example, changing the criterion of finding the optimal barrier and discussing under more extended risk models.