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A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes

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  • Gatto, Riccardo

Abstract

This article provides an importance sampling algorithm for computing the probability of ruin with recuperation of a spectrally negative Lévy risk process with light-tailed downwards jumps. Ruin with recuperation corresponds to the following double passage event: for some t∈(0,∞), the risk process starting at level x∈[0,∞) falls below the null level during the period [0,t] and returns above the null level at the end of the period t. The proposed Monte Carlo estimator is logarithmic efficient, as t,x→∞, when y=t/x is constant and below a certain bound.

Suggested Citation

  • Gatto, Riccardo, 2015. "A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 177-184.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:177-184
    DOI: 10.1016/j.spl.2015.01.019
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    1. Biffis, Enrico & Morales, Manuel, 2010. "On a generalization of the Gerber-Shiu function to path-dependent penalties," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 92-97, February.
    2. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
    3. Riccardo Gatto, 2010. "A Saddlepoint Approximation to the Distribution of Inhomogeneous Discounted Compound Poisson Processes," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 533-551, September.
    4. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
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