Retirement Wealth under Fixed Limits: The Optimal Strategy for Exponential Utility

TL;DR

This paper analyzes the optimal investment strategy for exponential utility investors under fixed wealth constraints in a Black-Scholes model, examining how these limits affect the distribution of terminal wealth through theoretical and quantitative methods.

Contribution

It introduces a framework for incorporating fixed wealth constraints into exponential utility maximization and explores their impact on the distribution of terminal wealth.

Findings

Constraints alter the distribution of terminal wealth.

Restricting to positive investments affects wealth outcomes.

Theoretical results are supported by quantitative examples.

Abstract

For an exponential utility maximizing investment strategy in a Black-Scholes Setting, fixed upper and lower constraints are introduced on the terminal wealth. This is equivalent to combining the optimal strategy with options. The resulting distribution is investigated in terms of change of quantiles. The theory is illustrated with quantitative examples, including an assessment of the effects of restricting the strategy to positive investments.