Optimal investment policy and dividend payment strategy in an insurance company

Pablo Azcue and Nora Muler

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Abstract: We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cram\'{e}r--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.

Date: 2010-10
New Economics Papers: this item is included in nep-ias
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Citations: View citations in EconPapers (15)

Published in Annals of Applied Probability 2010, Vol. 20, No. 4, 1253-1302

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