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Laplace transform of the survival probability under Sparre Andersen model

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Abstract

In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the survival probability is well given when the claim amount distribution is Erlang distribution or mixed Erlang distribution. The expressions for moments of the time to ruin with the model above are given.

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References

  1. Asmussen S. Probabilities. Singapore: World Scientific, 2000.

    Google Scholar 

  2. Cheng Y B, Tang Q H. Moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. North American Actuarial Journal, 2003, 7: 1–12.

    MATH  MathSciNet  Google Scholar 

  3. Dickson D C M, Hipp C. Ruin probabilities for Erlang(2) risk processes. Insurance: Mathematics Economics, 1998,22: 251–262.

    Google Scholar 

  4. Dickson D C M, Hipp C. On the time to ruin for Erlang(2) risk processes. Insurance: Mathematics Economics, 2001, 29: 333–344.

    Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  6. Gerber H U, Shiu E S W. The time value of ruin in a Sparre Andersen model. North American Actuarial Journal, 2005, 9: 49–84.

    MATH  MathSciNet  Google Scholar 

  7. Malinovskii V K. Non-Poissonian claims’ arrivals calculation of the probability of ruin. Insurance: Mathematics Economics, 1998, 22: 123–138.

    Google Scholar 

  8. Spiegel M R. Schaum’s Outline of Theory and Problems of Laplace Transforms. New York: Schaum, 1965.

    Google Scholar 

  9. Tijms H. Stochastic Models: An Algorithmic Approach, Chichester: Wiley, 1994.

    MATH  Google Scholar 

  10. Wang R M, Liu H F. On the ruin probability under a class of risk process. Austin Bulletin, 2002, 32(1): 81–90.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Qufu Normal University, Qufu, 273165, China

    Sun Chuanguang

  2. Deparment of Basic Science, Shandong Water Polytechnic, Rizhao, 276826, China

    Sun Chuanguang

Authors
  1. Sun Chuanguang
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Additional information

Supported by the NNSF of China(10471076), the NSF of Shandong Province(Y2004A06) and the Key Project of the Ministry of Education of China(206091).

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Sun, C. Laplace transform of the survival probability under Sparre Andersen model. Appl. Math. Chin. Univ. 22, 109–118 (2007). https://doi.org/10.1007/s11766-007-0014-y

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  • DOI: https://doi.org/10.1007/s11766-007-0014-y

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