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The dividend function in the jump-diffusion dual model with barrier dividend strategy

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Abstract

A dual model of the perturbed classical compound Poisson risk model is considered under a constant dividend barrier. A new method is used in deriving the boundary condition of the equation for the expectation function by studying the local time of a related process. We obtain the expression for the expected discount dividend function in terms of those in the corresponding perturbed compound Poisson risk model without barriers. A special case in which the gain size is phase-type distributed is illustrated. We also consider the existence of the optimal dividend level.

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References

  1. Gerber H U. An extension of the renewal equation and its application in the collective theory of risk[J]. Skandinavisk Aktuarietidskrift, 1970, 53:205–210.

    MathSciNet  Google Scholar 

  2. Gerber H U, Landry B. On the discounted penalty at ruin in a jump-diffusion and the perpetual put option[J]. Insurance: Mathematics and Economics, 1998, 22(3):263–276.

    Article  MATH  MathSciNet  Google Scholar 

  3. Chiu S N, Yin C C. The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion[J]. Insurance: Mathematics and Economics, 2003, 33(1):59–66.

    Article  MATH  MathSciNet  Google Scholar 

  4. Tsai C C L. On the discounted distribution functions of the surplus process perturbed by diffusion[J]. Insurance: Mathematics and Economics, 2001, 28(3):401–419.

    Article  MATH  MathSciNet  Google Scholar 

  5. Zhang C, Wang G. The joint density function of three characteristics on jump-diffusion risk process[J]. Insurance: Mathematics and Economics, 2003, 32(3):445–455.

    Article  MATH  MathSciNet  Google Scholar 

  6. De Finetti B. Su un’impostazione alternativa della teoria collettiva del rischio[C]. In: Proceedings of the Transactions of the XV International Congress of Actuaries, 1957, Vol. 2, 433–443.

    Google Scholar 

  7. Dickson D C M, Waters H. Some optimal dividends problems[J]. ASTIN Bulletin, 2004, 34(1):49–74.

    Article  MATH  MathSciNet  Google Scholar 

  8. Gerber H U. On the probability of ruin in the presence of a linear dividend barried[J]. Scandinavian Actuarial Journal, 1981, 2:105–115.

    MathSciNet  Google Scholar 

  9. Gerber H U, Shiu E S W. Optimal dividends: analysis with Brownian motion[J]. North American Actuarial Journal, 2004, 8(1):1–20.

    MATH  MathSciNet  Google Scholar 

  10. Li S, Garrido J. On a class of renewal risk models with a constant dividend barrier[J]. Insurance: Mathematics and Economics, 2004, 35(3):691–701.

    Article  MATH  MathSciNet  Google Scholar 

  11. Lin X S, Willmot G E, Drekic S. The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function[J]. Insurance: Mathematics and Economics, 2003, 33(3):551–566.

    Article  MATH  MathSciNet  Google Scholar 

  12. Avanzi B, Gerber H U, Shiu E S W. Optimal dividend in the dual model[J]. Insurance: Mathematics and Economics, 2007, 41(1):111–123.

    Article  MATH  MathSciNet  Google Scholar 

  13. Ioannis Karatzas, Steven E Shreve. Brownian motion and stochastic calculus[M]. New York: Springer-Verlag, c1988.

    Google Scholar 

  14. Daniel Revuz, Marc Yor. Continuous martingales and Brownian motion[M]. Berlin: Springer-Verlag, c1991.

    Google Scholar 

  15. Wang G, Wu R. Some distributions for the classical risk processes that is perturbed by diffusion[J]. Insurance: Mathematics and Economics, 2000, 26(1):15–24.

    Article  MATH  MathSciNet  Google Scholar 

  16. Wang G. A decomposition of the ruin probability for the risk process perturbed by diffusion[J]. Insurance: Mathematics and Economics, 2001, 28(1):49–59.

    Article  MATH  MathSciNet  Google Scholar 

  17. Tsai C C L, Willmot G E. A generalized defective renewal equation for the surplus process perturbed by diffusion[J]. Insurance: Mathematics and Economics, 2002, 30(1):51–66.

    Article  MATH  MathSciNet  Google Scholar 

  18. Asmussen S. Ruin probabilities[M]. Singapore: World Scientific Publishing Co Pte Ltd, 2000.

    Google Scholar 

  19. Asmussen S. Appied probabilty and queues[M]. New York: Springer-Verlag, 2003.

    Google Scholar 

  20. Asmussen S. Stationary distributions for fluid flow models with or without Brownian noise[J]. Stochastic Models, 1995, 11(1):21–49.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, P. R. China

    Bo Li  (李波) & Rong Wu  (吴荣)

Authors
  1. Bo Li  (李波)
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  2. Rong Wu  (吴荣)
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Corresponding author

Correspondence to Bo Li  (李波).

Additional information

Communicated by GUO Xing-ming

Project supported by the National Basic Research Program of China (973 Program) (No. 2007CB814905), the National Natural Science Foundation of China (No. 10571092), and the Research Fund of the Doctorial Program of Higher Education

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Li, B., Wu, R. The dividend function in the jump-diffusion dual model with barrier dividend strategy. Appl. Math. Mech.-Engl. Ed. 29, 1239–1249 (2008). https://doi.org/10.1007/s10483-008-0913-z

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  • DOI: https://doi.org/10.1007/s10483-008-0913-z

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Chinese Library Classification

2000 Mathematics Subject Classification

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