Risk Sensitive Control of the Lifetime Ruin Problem

TL;DR

This paper addresses a risk-sensitive control approach to the lifetime ruin problem, deriving an explicit solution for an asymptotically optimal investment policy in a Black-Scholes market setting.

Contribution

It introduces a differential game framework for the risk-sensitive lifetime ruin problem and provides an explicit solution for the asymptotically optimal policy.

Findings

Explicit solution for the differential game governing the problem

Asymptotically optimal investment policy derived

Framework applicable to Black-Scholes market scenarios

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.