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Optimal investment policy and dividend payment strategy in an insurance company

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  • Pablo Azcue
  • Nora Muler

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.

Suggested Citation

  • Pablo Azcue & Nora Muler, 2010. "Optimal investment policy and dividend payment strategy in an insurance company," Papers 1010.4988, arXiv.org.
  • Handle: RePEc:arx:papers:1010.4988
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    File URL: http://arxiv.org/pdf/1010.4988
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    References listed on IDEAS

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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. Chuancun Yin, 2013. "Optimal dividend problem for a generalized compound Poisson risk model," Papers 1305.1747, arXiv.org, revised Feb 2014.
    2. Andrea Barth & Santiago Moreno–Bromberg & Oleg Reichmann, 2016. "A Non-stationary Model of Dividend Distribution in a Stochastic Interest-Rate Setting," Computational Economics, Springer;Society for Computational Economics, vol. 47(3), pages 447-472, March.
    3. repec:eee:insuma:v:74:y:2017:i:c:p:31-45 is not listed on IDEAS
    4. 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.

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