Optimal Investment Strategy to Minimize Occupation Time

TL;DR

This paper derives an optimal investment strategy to minimize the expected duration of negative wealth, considering constant consumption and a Black-Scholes market, with an extension to penalize negative wealth duration.

Contribution

It introduces a novel approach to minimize occupation time in a stochastic investment setting, including a penalized extension for negative wealth periods.

Findings

Derived explicit optimal investment strategies.

Extended model with penalization for negative occupation time.

Provides insights into risk management for wealth depletion.

Abstract

We find the optimal investment strategy to minimize the expected time that an individual's wealth stays below zero, the so-called {\it occupation time}. The individual consumes at a constant rate and invests in a Black-Scholes financial market consisting of one riskless and one risky asset, with the risky asset's price process following a geometric Brownian motion. We also consider an extension of this problem by penalizing the occupation time for the degree to which wealth is negative.