Bankruptcy probabilities under non-Poisson inspection

TL;DR

This paper analyzes the probability of an insurance firm's surplus falling below zero under non-Poisson inspection times, providing explicit transforms, asymptotics, and an efficient simulation method.

Contribution

It introduces explicit transform expressions, establishes asymptotic results, and proposes an efficient importance sampling algorithm for non-Poisson inspection models.

Findings

Explicit transform formulas for various inter-inspection distributions

Cramér-Lundberg asymptotics for surplus ruin probabilities

Logarithmically efficient Monte Carlo simulation method

Abstract

This paper concerns an insurance firm's surplus process observed at renewal inspection times, with a focus on assessing the probability of the surplus level dropping below zero. For various types of inter-inspection time distributions, an explicit expression for the corresponding transform is given. In addition, Cram\'er-Lundberg type asymptotics are established. Also, an importance sampling based Monte Carlo algorithm is proposed, and is shown to be logarithmically efficient.