Minimizing the Expected Lifetime Spent in Drawdown Under Proportional Consumption
12 Pages Posted: 25 Aug 2015 Last revised: 26 Aug 2015
Date Written: August 21, 2015
We determine the optimal amount to invest in a Black-Scholes financial market for an individual who consumes at a rate equal to a constant proportion of her wealth and who wishes to minimize the expected time that her wealth spends in drawdown during her lifetime. Drawdown occurs when wealth is less than some fixed proportion of maximum wealth. We compare the optimal investment strategy with those for three related goal-seeking problems and learn that the individual is myopic in her investing behavior, as expected from other goal-seeking research.
Keywords: Drawdown, occupation time, optimal investment, stochastic control, free-boundary problem
JEL Classification: C61, G02, G11
Suggested Citation: Suggested Citation