Journal article

Optimal Dividends and Capital Injections in the Dual Model with a Random Time Horizon

Yongxia Zhao, Rongming Wang, Dingjun Yao, Ping Chen

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | SPRINGER/PLENUM PUBLISHERS | Published : 2015

Abstract

This paper investigates an optimal dividend and capital injection problem in the dual model with a random horizon. Both fixed and proportional costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends and the penalized discounted capital injections during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. By the fluctuation theory of Lévy 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 Lévy processes. Besides, numerical examples ..

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University of Melbourne Researchers

Grants

Awarded by National Natural Science Foundation of China


Awarded by Doctoral Program Foundation of the Ministry of Education of China


Funding Acknowledgements

The authors acknowledge the financial support of National Natural Science Foundation of China (11231005, 11101205, 11201123) and Doctoral Program Foundation of the Ministry of Education of China (20110076110004). The authors would like to thank the anonymous referees for helpful comments.