Ruin probabilities under general investments and heavy-tailed claims

TL;DR

This paper analyzes the asymptotic behavior of ruin probabilities for insurance companies with heavy-tailed claims, using general semimartingale models for risky asset investments and deriving large deviation results.

Contribution

It introduces a novel large deviation framework for ruin probabilities under broad investment models and heavy-tailed claims, extending previous results to general semimartingale settings.

Findings

Asymptotic decay of ruin probabilities characterized

Uniform large deviation results derived

Applicable to arbitrary and optimal investment strategies

Abstract

In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve according to quite general semimartingales. We show that the ruin problem corresponds to determining hitting probabilities for the solution to a randomly perturbed stochastic integral equation. We derive a large deviation result for the hitting probabilities that holds uniformly over a family of semimartingales and show that this result gives the asymptotic decay of finite time ruin probabilities under arbitrary investment strategies, including optimal investment strategies.