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Recursive Calculation of Survival Probabilities

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  • Dickson, David C. M.
  • Waters, Howard R.

Abstract

In this paper we present an algorithm for the approximate calculation of finite time survival probabilities for the classical risk model. We also show how this algorithm can be applied to the calculation of infinite time survival probabilities. Numerical examples are given and the stability of the algorithms is discussed.

Suggested Citation

  • Dickson, David C. M. & Waters, Howard R., 1991. "Recursive Calculation of Survival Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 199-221, November.
    • Handle: RePEc:cup:astinb:v:21:y:1991:i:02:p:199-221_00
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    Cited by:

    1. Mijatović, Aleksandar & Vidmar, Matija & Jacka, Saul, 2015. "Markov chain approximations to scale functions of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3932-3957.
    2. Ramsay, Colin M., 2003. "A solution to the ruin problem for Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 109-116, August.
    3. 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.
    4. Hailiang Yang & Lihong Zhang, 2006. "Ruin problems for a discrete time risk model with random interest rate," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 287-299, May.
    5. Cardoso, Rui M. R. & Egidio dos Reis, Alfredo D., 2002. "Recursive calculation of time to ruin distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 219-230, April.
    6. Cardoso, Rui M. R. & R. Waters, Howard, 2003. "Recursive calculation of finite time ruin probabilities under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 659-676, December.
    7. Cossette, Helene & Marceau, Etienne, 2000. "The discrete-time risk model with correlated classes of business," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 133-149, May.
    8. Yi Lu, 2016. "On the Evaluation of Expected Penalties at Claim Instants That Cause Ruin in the Classical Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 237-255, March.
    9. Stanford, David A. & Stroinski, Krzysztof J. & Lee, Karen, 2000. "Ruin probabilities based at claim instants for some non-Poisson claim processes," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 251-267, May.
    10. Yuen, Kam C. & Guo, Junyi & Wu, Xueyuan, 2006. "On the first time of ruin in the bivariate compound Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 298-308, April.
    11. Matija Vidmar, 2018. "Fluctuation Theory for Upwards Skip-Free Lévy Chains," Risks, MDPI, vol. 6(3), pages 1-24, September.
    12. Stéphane Loisel & Claude Lefèvre, 2009. "Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities," Post-Print hal-00201377, HAL.
    13. Andrius Grigutis & Jonas Šiaulys, 2020. "Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model," Mathematics, MDPI, vol. 8(2), pages 1-30, January.
    14. Dickson, David C. M. & Waters, Howard R., 1999. "Ruin probabilities with compounding assets," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 49-62, September.
    15. Marceau, Etienne & Rioux, Jacques, 2001. "On robustness in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 167-185, October.
    16. Dickson, David C. M. & Waters, Howard R., 1996. "Reinsurance and ruin," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 61-80, December.
    17. Egidio dos Reis, Alfredo D., 2000. "On the moments of ruin and recovery times," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 331-343, December.
    18. Frey, Andreas & Schmidt, Volker, 1996. "Taylor-series expansion for multivariate characteristics of classical risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 18(1), pages 1-12, May.
    19. Cossette, Hélène & Marceau, Etienne & Trufin, Julien & Zuyderhoff, Pierre, 2020. "Ruin-based risk measures in discrete-time risk models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 246-261.
    20. Jingchao Li & Bihao Su & Zhenghong Wei & Ciyu Nie, 2022. "A Multinomial Approximation Approach for the Finite Time Survival Probability Under the Markov-modulated Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2169-2194, September.
    21. Li Qin & Susan M. Pitts, 2012. "Nonparametric Estimation of the Finite-Time Survival Probability with Zero Initial Capital in the Classical Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 919-936, December.

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