OPTIMAL DIVIDENDS AND CAPITAL INJECTIONS FOR A SPECTRALLY POSITIVE LEVY PROCESS

摘要

This paper investigates an optimal dividend and capital injection problem for a spectrally positive Levy process, where the dividend rate is restricted. Both the ruin penalty and the costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends, the penalized discounted capital injections before ruin, and the expected discounted ruin penalty. By the fluctuation theory of Levy processes, the optimal dividend and capital injection strategy is obtained. We also find that the optimal return function can be expressed in terms of the scale functions of Levy processes. Besides, a series of numerical examples are provided to illustrate our consults.