Abstract
This paper investigates the dividend problem with non-exponential discounting in a dual model. We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable. Since the non-exponential discount function leads to a time inconsistent control problem, we study the equilibrium HJB-equation and give the associated verification theorem. For the case of a mixture of exponential discount functions and exponential gains, we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function. Besides, numerical examples are shown to illustrate our results.
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Supported by the Shandong Provincial Natural Science Foundation of China(ZR2020MA035 and ZR2023MA093).
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Zhao, Yx., Ye, Cx. & Cheng, Gp. Equilibrium dividend strategies in the dual model with a random time horizon. Appl. Math. J. Chin. Univ. 38, 510–522 (2023). https://doi.org/10.1007/s11766-023-3751-7
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DOI: https://doi.org/10.1007/s11766-023-3751-7
Keywords
- equilibrium dividend strategies
- non-exponential discounting
- time inconsistence
- dual model
- equilibrium HJB-equation