Minimizing the Probability of Lifetime Ruin under Stochastic Volatility

TL;DR

This paper develops a stochastic control framework to determine optimal investment strategies that minimize the probability of lifetime ruin in markets with stochastic volatility, reflecting real-world financial complexities.

Contribution

It introduces a novel approach to minimize lifetime ruin probability considering stochastic volatility, enhancing the realism of financial risk management models.

Findings

Optimal strategies derived for stochastic volatility models

Reduced probability of ruin with proposed control methods

Framework applicable to real-world financial planning

Abstract

We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following a diffusion with stochastic volatility. In the current financial market especially, it is important to include stochastic volatility in the risky asset's price process. Given the rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probability of going bankrupt. To solve this minimization problem, we use techniques from stochastic optimal control.