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Simulating the ruin probability of risk processes with delay in claim settlement

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  • Torrisi, G. L.

Abstract

A risk process with delay in claim settlement is usually described in terms of a Poisson shot-noise process (see Klüppelberg and Mikosch (Bernoulli 1 (1995) 125) and Brémaud (Appl. Probab. 37 (2000) 914)). In particular, proves that under suitable conditions the corresponding ruin probability goes to zero not slower than an exponential rate. This yields problems if we want to estimate the ruin probability by a Monte Carlo simulation. In this paper we overcome these difficulties deriving the asymptotically efficient simulation law.

Suggested Citation

  • Torrisi, G. L., 2004. "Simulating the ruin probability of risk processes with delay in claim settlement," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 225-244, August.
    • Handle: RePEc:eee:spapps:v:112:y:2004:i:2:p:225-244
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    References listed on IDEAS

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    1. Peter W. Glynn & Donald L. Iglehart, 1989. "Importance Sampling for Stochastic Simulations," Management Science, INFORMS, vol. 35(11), pages 1367-1392, November.
    2. Macci Claudio, 2001. "Simulating Level Crossing Probabilities By Importance Sampling For Non-Decreasing Compound Poisson Processes With Bounded Jumps And A Negative Drift," Statistics & Risk Modeling, De Gruyter, vol. 19(2), pages 191-202, February.
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    Cited by:

    1. Bohan Chen & Jose Blanchet & Chang-Han Rhee & Bert Zwart, 2019. "Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 919-942, August.
    2. Chengguo Weng & Yi Zhang & Ken Seng Tan, 2013. "Tail Behavior of Poisson Shot Noise Processes under Heavy-tailed Shocks and Actuarial Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 655-682, September.
    3. Jang, Jiwook & Dassios, Angelos & Zhao, Hongbiao, 2018. "Moments of renewal shot-noise processes and their applications," LSE Research Online Documents on Economics 87428, London School of Economics and Political Science, LSE Library.
    4. Torrisi, Giovanni Luca & Leonardi, Emilio, 2022. "Asymptotic analysis of Poisson shot noise processes, and applications," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 229-270.
    5. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 55-65.
    6. Stabile, Gabriele & Torrisi, Giovanni Luca, 2010. "Large deviations of Poisson shot noise processes under heavy tail semi-exponential conditions," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1200-1209, August.
    7. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," LSE Research Online Documents on Economics 64051, London School of Economics and Political Science, LSE Library.

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