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Insurance control for classical risk model with fractional Brownian motion perturbation

Author

Listed:
  • Zhang, H.Y.
  • Bai, L.H.
  • Zhou, A.M.

Abstract

In the paper, we consider a classical risk model that is perturbed by a standard fractional Brownian motion with Hurst parameter . The customers' input may be considered as a control parameter which allows the firm to reach a desired target at a specified time. By using the completion of squares method, we obtain an expression of the optimal value function and the corresponding optimal control policy.

Suggested Citation

  • Zhang, H.Y. & Bai, L.H. & Zhou, A.M., 2009. "Insurance control for classical risk model with fractional Brownian motion perturbation," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 473-480, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:4:p:473-480
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    References listed on IDEAS

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    1. Rimas Norvaisa, 2000. "Modelling of stock price changes: A real analysis approach," Finance and Stochastics, Springer, vol. 4(3), pages 343-369.
    2. N. E. Frangos & S. D. Vrontos & A. N. Yannacopoulos, 2007. "Reinsurance control in a model with liabilities of the fractional Brownian motion type," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(5), pages 403-428, September.
    3. Biagini, Francesca & Hu, Yaozhong & Øksendal, Bernt & Sulem, Agnès, 0. "A stochastic maximum principle for processes driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 233-253, July.
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