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On the evaluation of finite-time ruin probabilities in a dependent risk model

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  • Dimitrova, Dimitrina S.
  • Kaishev, Vladimir K.
  • Zhao, Shouqi

Abstract

This paper establishes some enlightening connections between the explicit formulas of the finite-time ruin probability obtained by Ignatovand Kaishev (2000, 2004) and Ignatov et al. (2001) for a risk model allowing dependence. The numerical properties of these formulas are investigated and efficient algorithms for computing ruin probability with prescribed accuracy are presented. Extensive numerical comparisons and examples are provided.

Suggested Citation

  • Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Zhao, Shouqi, 2016. "On the evaluation of finite-time ruin probabilities in a dependent risk model," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 268-286.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:268-286
    DOI: 10.1016/j.amc.2015.11.082
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    3. Stéphane Loisel & Claude Lefèvre, 2009. "Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities," Post-Print hal-00201377, HAL.
    4. Claude Lefèvre & Stéphane Loisel, 2009. "Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 425-441, September.
    5. Lefèvre, Claude & Picard, Philippe, 2011. "A new look at the homogeneous risk model," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 512-519.
    6. Cossette, Hélène & Marceau, Etienne & Marri, Fouad, 2008. "On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 444-455, December.
    7. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 245-254, October.
    8. Ignatov, Zvetan G. & Kaishev, Vladimir K. & Krachunov, Rossen S., 2001. "An improved finite-time ruin probability formula and its Mathematica implementation," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 375-386, December.
    9. Garcia, Jorge M.A., 2005. "Explicit Solutions for Survival Probabilities in the Classical Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 113-130, May.
    10. Das, S. & Kratz, M., 2012. "Alarm system for insurance companies: A strategy for capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 53-65.
    11. Kaishev, Vladimir K. & Dimitrova, Dimitrina S., 2006. "Excess of loss reinsurance under joint survival optimality," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 376-389, December.
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    Cited by:

    1. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. Dimitrina S. Dimitrova & Zvetan G. Ignatov & Vladimir K. Kaishev, 2017. "On the First Crossing of Two Boundaries by an Order Statistics Risk Process," Risks, MDPI, vol. 5(3), pages 1-14, August.
    3. Pierre-Olivier Goffard, 2019. "Two-Sided Exit Problems in the Ordered Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 539-549, June.
    4. Pierre-Olivier Goffard, 2019. "Fraud risk assessment within blockchain transactions," Working Papers hal-01716687, HAL.
    5. Dimitrina S. Dimitrova & Zvetan G. Ignatov & Vladimir K. Kaishev, 2019. "Ruin and Deficit Under Claim Arrivals with the Order Statistics Property," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 511-530, June.

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