Proportional reinsurance for fractional Brownian risk model

TL;DR

This paper analyzes ruin probabilities in a two-dimensional fractional Brownian risk model with proportional reinsurance, deriving asymptotic results for large initial capital in a finite-time horizon.

Contribution

It introduces a fractional Brownian risk model with proportional reinsurance and derives asymptotic ruin probabilities for joint and simultaneous ruin events.

Findings

Asymptotic ruin probabilities are derived for large initial capital.

The model accounts for dependence via fractional Brownian motion.

Results apply to finite-time horizon risk assessments.

Abstract

This paper investigates ruin probabilities for a two-dimensional fractional Brownian risk model with a proportional reinsurance scheme. We focus on joint and simultaneous ruin probabilities in a finite-time horizon. The risk processes of both insurance and reinsurance companies are composed of a large number of i.i.d. sub-risk processes, representing independent businesses. We derive the asymptotics as the initial capital tends to infinity.