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

Riccardo Gatto

Statistics & Probability Letters, 2015, vol. 99, issue C, 177-184

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.

Keywords: Esscher approximation; Exponential tilt; Monte Carlo simulation; Importance sampling; Legendre–Fenchel transform (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.01.019

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