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

作者：Gatto Riccardo^*

来源：Statistics & Probability Letters, 2015, 99: 177-184.

DOI：10.1016/j.spl.2015.01.019

• Esscher approximation
• Exponential tilt
• Monte Carlo simulation
• Importance sampling
• Legendre-Fenchel transform

This article provides an importance sampling algorithm for computing the probability of ruin with recuperation of a spectrally negative Levy risk process with light-tailed downwards jumps. Ruin with recuperation corresponds to the following double passage event: for some t is an element of (0, infinity), the risk process starting at level x is an element of [0, infinity) 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 -> infinity, when y = t/x is constant and below a certain bound.

• 出版日期2015-4