On ruin probabilities with risky investments

TL;DR

This paper analyzes the asymptotic behavior of ruin probabilities for insurance companies with mixed insurance lines investing in risky assets with stochastic volatility, using implicit renewal theory to determine convergence rates.

Contribution

It introduces a novel approach to evaluate ruin probabilities in a complex setting involving stochastic volatility and Markov-driven parameters.

Findings

Derived the rate of convergence to zero of ruin probabilities.

Applied implicit renewal theory to a new class of stochastic models.

Provided insights into risk management for insurance with risky investments.

Abstract

We investigate the asymptotic of ruin probabilities when the company combines the life- and non-life insurance businesses and invests its reserve into a risky asset with stochastic volatility and drift driven by a two-state Markov process. Using the technique of the implicit renewal theory we obtain the rate of convergence to zero of the ruin probabilities.