Optimal dividend policies for compound Poisson processes: The case of bounded dividend rates

Pablo Azcue and Nora Muler

Insurance: Mathematics and Economics, 2012, vol. 51, issue 1, 26-42

Abstract: We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cramér–Lundberg model with arbitrary claim-size distribution. Our objective is to find the dividend payment policy which maximizes the cumulative expected discounted dividend pay-outs until the time of bankruptcy imposing a ceiling on the dividend rates. We characterize the optimal value function as the unique bounded viscosity solution of the associated Hamilton–Jacobi–Bellman equation. We prove that there exists an optimal dividend strategy and that this strategy is stationary with a band structure. We study the regularity of the optimal value function. We find a characterization result to check optimality even in the case where the optimal value function is not differentiable. We construct examples where the claim-size distribution is smooth but the optimal dividend policy is not threshold and the optimal value function is not differentiable. We study the survival probability of the company under the optimal dividend policy. We also present examples where the optimal dividend policy has infinitely many bands even in the case that the claim-size distribution has a bounded density.

Keywords: Cramér–Lundberg process; Insurance; Bounded dividend rates; Optimal investment policy; Hamilton–Jacobi–Bellman equation; Viscosity solution; Risk control; Threshold strategy; Band strategy (search for similar items in EconPapers)
JEL-codes: G22 G35 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:51:y:2012:i:1:p:26-42

DOI: 10.1016/j.insmatheco.2012.02.011

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