Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs |
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| Institution: | 1. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, PR China;2. School of Management, University of China Academy of Sciences, Beijing 100190, PR China;3. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia;1. Department of Mathematics, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany;2. Wroc?aw University of Technology, PL-50-370 Wroc?aw, Poland |
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| Abstract: | We consider an optimal impulse control problem on reinsurance, dividend and reinvestment of an insurance company. To close reality, we add fixed and proportional transaction costs to this problem. The value of the company is associated with expected present value of net dividends pay out minus the net reinvestment capitals until ruin time. We focus on non-cheap proportional reinsurance. We prove that the value function is a unique solution to associated Hamilton–Jacobi–Bellman equation, and establish the regularity property of the viscosity solution under a weak assumption. We solve the non-uniformly elliptic equation associated with the impulse control problem. Finally, we derive the value function and the optimal strategy of the control problem. |
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| Keywords: | Optimal impulse control Optimal dividend and reinvestment Non-uniformly elliptic equation Viscosity solution Fixed and proportional transaction costs Proportional reinsurance |
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