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Optimal investment policy and dividend payment strategy in an insurance company

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  • Pablo Azcue
  • 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.

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    File URL: http://arxiv.org/pdf/1010.4988
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1010.4988.

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    Date of creation: Oct 2010
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    Publication status: Published in Annals of Applied Probability 2010, Vol. 20, No. 4, 1253-1302
    Handle: RePEc:arx:papers:1010.4988

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    Web page: http://arxiv.org/

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    1. S. P. Sethi & N. A. Derzko & J. P. Lehoczky, 1991. "A Stochastic Extension of the Miller-Modigliani Framework," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 57-76.
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    Cited by:
    1. Yin, Chuancun & Yuen, Kam Chuen, 2011. "Optimality of the threshold dividend strategy for the compound Poisson model," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1841-1846.
    2. Chuancun Yin, 2013. "Optimal dividend problem for a generalized compound Poisson risk model," Papers 1305.1747, arXiv.org, revised Feb 2014.

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