Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs

Huiqi Guan and Zongxia Liang

Insurance: Mathematics and Economics, 2014, vol. 54, issue C, 109-122

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.

Keywords: Optimal impulse control; Optimal dividend and reinvestment; Non-uniformly elliptic equation; Viscosity solution; Fixed and proportional transaction costs; Proportional reinsurance (search for similar items in EconPapers)
JEL-codes: C61 G11 G22 G32 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:54:y:2014:i:c:p:109-122

DOI: 10.1016/j.insmatheco.2013.11.003

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