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Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation

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  • Zhuo Jin
  • George Yin
  • Chao Zhu
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    Abstract

    This paper develops numerical methods for finding optimal dividend pay-out and reinsurance policies. A generalized singular control formulation of surplus and discounted payoff function are introduced, where the surplus is modeled by a regime-switching process subject to both regular and singular controls. To approximate the value function and optimal controls, Markov chain approximation techniques are used to construct a discrete-time controlled Markov chain with two components. The proofs of the convergence of the approximation sequence to the surplus process and the value function are given. Examples of proportional and excess-of-loss reinsurance are presented to illustrate the applicability of the numerical methods.

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    File URL: http://arxiv.org/pdf/1111.2584
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    Paper provided by arXiv.org in its series Papers with number 1111.2584.

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    Date of creation: Nov 2011
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    Handle: RePEc:arx:papers:1111.2584

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    Web page: http://arxiv.org/

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    1. T. Choulli & M. Taksar & X. Y. Zhou, 2001. "Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(6), pages 573-596.
    2. Bjarne Højgaard & Søren Asmussen & Michael Taksar, 2000. "Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation," Finance and Stochastics, Springer, Springer, vol. 4(3), pages 299-324.
    3. Alvarez, Luis H. R., 2000. "Singular stochastic control in the presence of a state-dependent yield structure," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 86(2), pages 323-343, April.
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