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

Yongxia Zhao (), Rongming Wang (), Dingjun Yao and Ping Chen
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Yongxia Zhao: Qufu Normal University
Rongming Wang: East China Normal University
Dingjun Yao: Nanjing University of Finance and Economics
Ping Chen: University of Melbourne

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 1, No 13, 272-295

Abstract: 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 are studied to illustrate our results.

Keywords: Dividend; Capital injection; Dual model; Scale function; 60G51; 93E20 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-014-0653-0

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