Minimizing Lifetime Poverty with a Penalty for Bankruptcy

TL;DR

This paper develops a model for optimal investment strategies aimed at minimizing lifetime poverty, incorporating penalties for bankruptcy, and generalizes existing ruin and occupation minimization problems.

Contribution

It introduces a generalized framework using a poverty function to unify and extend previous models of lifetime ruin and occupation minimization.

Findings

Derived optimal investment strategies for specific poverty and consumption functions.

Proved properties of the optimal strategies under the proposed model.

Connected poverty minimization with classical ruin problems.

Abstract

We provide investment advice for an individual who wishes to minimize her lifetime poverty, with a penalty for bankruptcy or ruin. We measure poverty via a non-negative, non-increasing function of (running) wealth. Thus, the lower wealth falls and the longer wealth stays low, the greater the penalty. This paper generalizes the problems of minimizing the probability of lifetime ruin and minimizing expected lifetime occupation, with the poverty function serving as a bridge between the two. To illustrate our model, we compute the optimal investment strategies for a specific poverty function and two consumption functions, and we prove some interesting properties of those investment strategies.