Optimal periodic dividend and capital injection problem for spectrally positive Lévy processes

By Yongxia Zhao, Ping Chen, Hailiang Yang. 2017

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Abstract In this paper, we investigate an optimal periodic dividend and capital injection problem for spectrally positive Levy processes. We assume that the periodic dividend strategy has exponential inter-dividend-decision times and continuous monitoring of solvency. Both proportional and fixed transaction costs from capital injection are considered. The objective is to maximize the total value of the expected discounted dividends and the penalized discounted capital injections until the time of ruin. By the fluctuation theory of Levy processes in Albrecher et al. (2016), the optimal periodic dividend and capital injection strategies are derived. We also find that the optimal return function can be expressed in terms of the scale functions of Levy processes. Finally, numerical examples are studied to illustrate our results.

Subfields: Demography, Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/31dccc16b9c3f39c1e7dd7007aaafe9a1da8d96f