On the Optimal Dividend Problem for the Dual Jump-Diffusion Model

How to distribute dividends to shareholders of a company so that the expectation of the discounted dividends can be maximized is a classical actuarial problem. Different from many papers which focus on the insurance company, this paper discusses the optimal dividend problem for another kind of company, which specializes in inventions and discovers and thus has occasional gains and constant expense rate. The reserve of such company is described as a dual jump-diffusion model. We find the optimality conditions under which a barrier strategy is optimal among all admissible policies. Moreover, in the special case that gains jumps come from a compound Poisson process with mixtures of exponential distributions, the optimal policy is proved to take the form of a barrier strategy. Finally, some sensitivity analysis to the model parameters is provided.