Risk Sensitive Control of the Lifetime Ruin Problem

Abstract

We study a risk sensitive control version of the lifetime ruin probability problem. We consider a sequence of investments problems in Black-Scholes market that includes a risky asset and a riskless asset. We present a differential game that governs the limit behavior. We solve it explicitly and use it in order to find an asymptotically optimal policy.

Final version. To appear in Applied Mathematics and Optimization. Keywords: Probability of lifetime ruin, optimal investment, risk sensitive control, large deviations, differential games