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

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.