The Annals of Applied Probability

Optimal investment policy and dividend payment strategy in an insurance company

Pablo Azcue and Nora Muler

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We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cramér–Lundberg process. The firm has the option of investing part of the surplus in a Black–Scholes financial market. The objective is to find a strategy consisting of both investment and dividend payment policies which maximizes the cumulative expected discounted dividend pay-outs until the time of bankruptcy. We show that the optimal value function is the smallest viscosity solution of the associated second-order integro-differential Hamilton–Jacobi–Bellman equation. We study the regularity of the optimal value function. We show that the optimal dividend payment strategy has a band structure. We find a method to construct a candidate solution and obtain a verification result to check optimality. Finally, we give an example where the optimal dividend strategy is not barrier and the optimal value function is not twice continuously differentiable.

Article information

Ann. Appl. Probab., Volume 20, Number 4 (2010), 1253-1302.

First available in Project Euclid: 20 July 2010

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Zentralblatt MATH identifier

Primary: 91B30: Risk theory, insurance
Secondary: 91B28 91B70: Stochastic models 49L25: Viscosity solutions

Cramér–Lundberg process insurance dividend payment strategy optimal investment policy Hamilton–Jacobi–Bellman equation viscosity solution risk control dynamic programming principle band strategy barrier strategy


Azcue, Pablo; Muler, Nora. Optimal investment policy and dividend payment strategy in an insurance company. Ann. Appl. Probab. 20 (2010), no. 4, 1253--1302. doi:10.1214/09-AAP643.

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