Maximizing Utility of Consumption Subject to a Constraint on the Probability of Lifetime Ruin

TL;DR

This paper explicitly solves a consumption utility maximization problem with a lifetime ruin probability constraint, integrating risk management into optimal consumption strategies over an individual's lifetime.

Contribution

It provides an explicit solution to a novel problem combining utility maximization with lifetime ruin probability constraints.

Findings

Explicit solution to the constrained optimization problem

Incorporation of lifetime ruin probability as a risk measure

Enhanced understanding of optimal consumption under risk constraints

Abstract

In this note, we explicitly solve the problem of maximizing utility of consumption (until the minimum of bankruptcy and the time of death) with a constraint on the probability of lifetime ruin, which can be interpreted as a risk measure on the whole path of the wealth process.