The probability of exceeding a piecewise deterministic barrier by the heavy-tailed renewal compound process

TL;DR

This paper investigates the asymptotic probability of a heavy-tailed renewal process crossing a piecewise linear barrier, with applications to ruin probabilities in insurance risk management.

Contribution

It provides new asymptotic results for the crossing probabilities of heavy-tailed renewal processes over piecewise barriers, relevant for insurance risk analysis.

Findings

Derived asymptotic formulas for crossing probabilities

Applied results to ruin probabilities of insurance companies

Enhanced understanding of heavy-tailed process behaviors

Abstract

We analyze the asymptotics of crossing a high piecewise linear barriers by a renewal compound process with the subexponential jumps. The study is motivated by ruin probabilities of two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions when the initial reserves of both companies tend to infinity.