Abstract
<p style='text-indent:20px;'>In the dual risk model, we study the periodic dividend problem with a non-exponential discount function which results in a time-inconsistent control problem. Viewing it within the game theoretic framework, we extend the Hamilton-Jacobi-Bellman (HJB) system of equations from the fixed terminal to the time of ruin and derive the verification theorem, and we generalize the theory of classical optimal periodic dividend. Under two special non-exponential discount functions, we obtain the closed-form expressions of equilibrium strategy and the corresponding equilibrium value function in a compound Poisson dual model. Finally, some numerical examples are presented to illustrate the impact of some parameters.
Highlights
The spectrally positive Levy model, known as the dual model, is suitable for modeling companies such as pharmaceuticals and petroleum, and these companies occasionally benefit
We only prove that πis the equilibrium control law which is defined by Definition 2.2
We find that the equilibrium dividend barrier b increases at the beginning and decreases with the increase of parameter c, which is identified with the classical optimal dividend problem
Summary
The spectrally positive Levy model, known as the dual model, is suitable for modeling companies such as pharmaceuticals and petroleum, and these companies occasionally benefit. Time-inconsistent optimal control, Non-exponential discounting, Equilibrium periodic dividend strategy, Extended HJB system of equations, Levy process. Zhao et al [30] considers the optimal periodic dividend strategy and value function by the fluctuation theory of Levy processes.
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