On ruin probabilities with investments in a risky asset with a switching regime price

TL;DR

This paper analyzes the asymptotic behavior of ruin probabilities for companies investing in a risky asset with regime switching, showing how these probabilities diminish as initial capital increases, using renewal theory techniques.

Contribution

It introduces a model with regime-switching geometric Brownian motion for asset prices and derives the convergence rate of ruin probabilities using implicit renewal theory.

Findings

Ruin probabilities tend to zero as initial capital increases.

The convergence rate is explicitly characterized.

The model accounts for regime-dependent asset dynamics.

Abstract

We investigate the asymptotic of ruin probabilities when the company invests its reserve in a risky asset with a switching regime price. We assume that the asset price is a conditional geometric Brownian motion with parameters modulated by a Markov process with a finite number of states. Using the technique of the implicit renewal theory we obtain the rate of convergence to zero of the ruin probabilities as the initial capital tends to infinity.