An optimal dividend strategy in the discrete Sparre Andersen model with bounded dividend rates

Authors:
Jiyang Tan;Pingtian Yuan;Yangjin Cheng;Ziqiang Li
Affiliations:
-;-;-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2014

Citing 5
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Abstract

We consider the discrete Sparre Andersen risk model and its derivative models by anew setting up the initial times, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant. The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique bounded solution of a set of discrete Hamilton-Jacobi-Bellman equations. Moreover, we introduce Bellman's recursive algorithm and offer a simpler algorithm to obtain the optimal strategy and the optimal value functions. Our method is mainly to transform the value functions. Numerical examples are presented to illustrate the transformation method.