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On the Evaluation of Expected Penalties at Claim Instants That Cause Ruin in the Classical Risk Model

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References

  • Avram F, Usábel M (2003) Finite time ruin probabilities with one Laplace inversion. Insur Math Econ 32:371–377

    Article  MathSciNet  MATH  Google Scholar 

  • Avram F, Usábel M (2004) Ruin probabilities and deficit for the renewal risk model with phase-type interarrival times. ASTIN Bull 34:245–254

    Article  MathSciNet  MATH  Google Scholar 

  • De Vylder FE, Goovaerts MJ (1999) Explicit finite-time and infinite-time ruin probabilities in the continuous case. Insur Math Econ 24:155–172

    Article  MathSciNet  MATH  Google Scholar 

  • Dickson DCM (1999) On numerical evaluation of finite time survival probabilities. r Actuar J 5:575–584

    Article  Google Scholar 

  • Dickson DCM (2012) The joint distribution of the time to ruin and the number of claims until ruin in the classical risk model. Insur Math Econ 50(3):334–337

    Article  MathSciNet  MATH  Google Scholar 

  • Dickson DCM, Hipp C (2001) On the time to ruin for Erlang(2) risk process. Insur Math Econ 29(3):333–344

    Article  MathSciNet  MATH  Google Scholar 

  • Dickson DCM, Waters HR (1991) Recursive calculation of survival probabilities. ASTIN Bull 21(2):199–221

    Article  Google Scholar 

  • Egidio dos Reis AD (2002) How many claims does it take to get ruined and recovered? Insur Math Econ 31(2):235–248

    Article  MathSciNet  MATH  Google Scholar 

  • Garcia JMA (2005) Explicit solutions for survival probabilities in the classical risk model. ASTIN Bull 35(1):113–130

    Article  MathSciNet  MATH  Google Scholar 

  • Gerber HU (1979) An introduction to mathematical risk theory. S.S. Huebner Foundation Monographs, University of Pennsylvania

  • Gerber HU, Shiu ESW (1998) On the time value of ruin. North American Actuar J 2(1):48–72

    Article  MathSciNet  MATH  Google Scholar 

  • Gerber HU, Shiu ESW (2005) The time value of ruin in a Sparre Andersen model. North American Actuar J 9(2):49–69

    Article  MathSciNet  MATH  Google Scholar 

  • Landriault D, Shi T, Willmot GE (2011) Joint densities involving the time to ruin in the Sparre Andersen risk model under exponential assumptions. Insur Math Econ 49(3):371–379

    Article  MathSciNet  MATH  Google Scholar 

  • Lefèvre C, Loisel S (2008) On finite-time ruin probabilities for classical risk models. Scand Actuar J 1:41–60

    Article  MathSciNet  MATH  Google Scholar 

  • Li S, Garrido J (2004) On ruin for the Erlang(n) risk process. Insur Math Econ 34(3):391–408

    Article  MathSciNet  MATH  Google Scholar 

  • McCurdy A, Ng KC, Parlett BN (1984) Accurate computation of divided differences of the exponential function. Math Computat 43(168):501–528

    Article  MathSciNet  MATH  Google Scholar 

  • Picard P, Lefèvre C (1997) The probability of ruin in finite-time with discrete claim size distribution. Scand Actuar J 1:58–69

    Article  MathSciNet  MATH  Google Scholar 

  • Rolski T, Schmidli H, Schmidt V, Teugels J (1999) Stochastic processes for insurance and finance. Wiley, Chichester

    Book  MATH  Google Scholar 

  • Stanford DA, Stroïnski KJ (1994) Recursive methods for computing finite-time ruin probabilities for phase-distributed claim sizes. ASTIN Bull 24(2):235–254

    Article  Google Scholar 

  • Stanford DA, Stroïnski KJ, Lee K (2000) Ruin probabilities based at claim instants for some non-Poisson claim processes. Insur Math Econ 26(2–3):251–267

    Article  MathSciNet  MATH  Google Scholar 

  • Willmot GE (2007) On the discounted penalty function in the renewal risk model with general interclaim times. Insur Math Econ 41(1):17–31

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The author would like to thank two anonymous reviewers for their constructive comments for improving the paper and Dr. Shuanming Li for insightful discussions on the topic. This research was supported by the Natural Science and Engineering Research Council (NSERC) of Canada.

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  1. Department of Statistics & Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada, V5A 1S6

    Yi Lu

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  1. Yi Lu
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Lu, Y. On the Evaluation of Expected Penalties at Claim Instants That Cause Ruin in the Classical Risk Model. Methodol Comput Appl Probab 18, 237–255 (2016). https://doi.org/10.1007/s11009-014-9413-8

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