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Some Results behind Dividend Problems

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Abstract

We consider the basic dividend problem of the compound Poisson model with constant barrier strategy. Some results concealed behind the dividend problem are made explicit in the present work. Different methods and some of which are firstly given in this paper. All these results presented certain direct relationship between some important actuary variables in classical risk theory is also revealed.

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References

  1. Albrecher, H., Graz, R.K. Risk theory with a nonlinear dividend barrier. Computing 68:289–311 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Asmussen, S. Ruin probability. World Scientific, Singapore, 2000

  3. Bühlmann, H. Mathematical methods in risk theory. Springer-Verlag, New York, 1970

  4. De Finetti, Bruno. Su un’impostazione alternativa dell teoria collettiva del rischio. Transactions of the XV th international Congress of Actraries, 2:433–443 (1957)

    Google Scholar 

  5. Dickson, D.C.M. Insurance Risk and Ruin. Cambridge University Press, London, 2005

  6. Dickson, D.C.M., Waters, H. Some optimal dividends problems. ASTIN Bulletin, 34:49–74 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gerber, H.U. An introduction to mathematical risk theory. The S.S. Huebner Foundation for Educational University of Pennsylvania, 1979

  8. Gerber, H.U. On the probability of ruin in the presence of a linear dividend barrier. Scand. Actuar. J. 2:105–115 (1981)

    MathSciNet  Google Scholar 

  9. Gerber, H.U. When does the surplus reach a given target? Insurance:Mathematics and Economics 9:115–119 (1990)

    Article  MathSciNet  Google Scholar 

  10. Gerber, H.U., Shiu, E.S.W. On the time value of ruin. North American Actuarial Journal, 2:48–78 (1998)

    MATH  MathSciNet  Google Scholar 

  11. Gerber, H.U., Shiu, E.S.W. On optimal dividend strategies in the compound Poisson model. North American Actuarial Journal, to appear, 2006

  12. Gerber, H.U., Shiu, E.S.W., Smith, N. Maximizing dividends without bankruptcy. North American Actuarial Journal, to appear, 2006

  13. 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. Insurace: Mathematics and Economic , 33:551–566 (2003)

    Article  MATH  Google Scholar 

  14. Revuz, D., Yor, M. Continuous Martingale and Brownian Motion. Springer-Verlag, Berlin, 1991

  15. Siegl, T., Tichy, R. A process with stochastic claim frequency and a linear dividend barrier. Insurace: Mathematics and Economics, 24:51–65 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  16. Wei, L., Wu, R. The joint distributions of several important actuarial diagnostics in the classical risk model. Insurace: Mathematics and Economic, 30:451–462 (2002)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Science, Nankai University, Tianjin, 300071, China

    Ming Zhou & Jun-yi Guo

  2. School of Finance, Renmin University of China, Beijing, 100872, China

    Li Wei

Authors
  1. Ming Zhou
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  2. Li Wei
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  3. Jun-yi Guo
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Corresponding author

Correspondence to Ming Zhou.

Additional information

Supported by the National Natural Science Foundation of China (No. 70501028, No. 10571092).

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Zhou, M., Wei, L. & Guo, Jy. Some Results behind Dividend Problems. Acta Math. Appl. Sin, Engl. Ser. 22, 681–686 (2006). https://doi.org/10.1007/s10255-006-0342-3

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  • DOI: https://doi.org/10.1007/s10255-006-0342-3

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