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

Gatto, Riccardo (2015). A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes. Statistics & probability letters, 99, pp. 177-184. North-Holland 10.1016/j.spl.2015.01.019

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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,∞)t∈(0,∞), the risk process starting at level x∈[0,∞)x∈[0,∞) falls below the null level during the period [0,t][0,t] and returns above the null level at the end of the period tt. The proposed Monte Carlo estimator is logarithmic efficient, as t,x→∞t,x→∞, when y=t/xy=t/x is constant and below a certain bound.

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