Equilibrium Dividend Strategy with Non-exponential Discounting in a Dual Model

Yongwu Li (), Zhongfei Li () and Yan Zeng ()
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Yongwu Li: Lanzhou University
Zhongfei Li: Sun Yat-sen University
Yan Zeng: Lingnan (University) College, Sun Yat-sen University

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 2, No 18, 699-722

Abstract: Abstract This paper studies an optimal dividend problem for a company with non-exponential discounting. The surplus process is described by a dual model, and the target is to find a dividend strategy that maximizes the expected discounted value of dividends until ruin. The non-exponential discount function leads to a time-inconsistent problem. We aim at seeking the equilibrium strategy derived by taking our problem as a non-cooperate game, which is a time-consistent strategy. An extended Hamilton–Jacobi–Bellman equation system and a verification theorem are provided to derive the equilibrium strategy and the equilibrium value function. For the case of pseudo-exponential discount function, closed-form expressions for the equilibrium strategy and the equilibrium value function are derived. In addition, some numerical illustrations of our results are showed.

Keywords: Non-exponential discount function; Equilibrium strategy; Dividend payment; Dual model; Hamilton–Jacobi–Bellman equation; 91G10; 93E20; 91A10; 60H20 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-015-0742-8

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