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Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments

Author

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  • Sooie-Hoe Loke

    (Department of Mathematics, Central Washington University, 400 East University Way, Ellensburg, WA 98926, USA)

  • Enrique Thomann

    (Department of Mathematics, Oregon State University, Corvallis, OR 97331-4605, USA)

Abstract

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability can be well approximated for any gain distributions. Examples involving exponential, uniform, Pareto and discrete gains are considered. Finally, the same numerical method is applied to the Laplace transform of the time of ruin.

Suggested Citation

  • Sooie-Hoe Loke & Enrique Thomann, 2018. "Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments," Risks, MDPI, vol. 6(4), pages 1-13, October.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:4:p:110-:d:173250
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    References listed on IDEAS

    as
    1. Jun Cai & Runhuan Feng & Gordon E. Willmot, 2009. "The Compound Poisson Surplus Model with Interest and Liquid Reserves: Analysis of the Gerber–Shiu Discounted Penalty Function," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 401-423, September.
    2. Yang, Yang & Wang, Yuebao, 2010. "Asymptotics for ruin probability of some negatively dependent risk models with a constant interest rate and dominatedly-varying-tailed claims," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 143-154, February.
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    6. Avanzi, Benjamin & U. Gerber, Hans & S.W. Shiu, Elias, 2007. "Optimal dividends in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 111-123, July.
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    Cited by:

    1. Julia Adamska & Łukasz Bielak & Joanna Janczura & Agnieszka Wyłomańska, 2022. "From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t -Distribution Case," Mathematics, MDPI, vol. 10(18), pages 1-29, September.
    2. Jiandong Ren & Kristina Sendova & Ričardas Zitikis, 2019. "Special Issue “Risk, Ruin and Survival: Decision Making in Insurance and Finance”," Risks, MDPI, vol. 7(3), pages 1-7, September.

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