Minimizing the Expected Lifetime Spent in Drawdown Under Proportional Consumption

12 Pages Posted: 25 Aug 2015 Last revised: 26 Aug 2015

Bahman Angoshtari

University of Michigan at Ann Arbor - Department of Mathematics

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

V.R. Young

University of Michigan at Ann Arbor - Department of Mathematics

Date Written: August 21, 2015

Abstract

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

Angoshtari, Bahman and Bayraktar, Erhan and Young, V.R., Minimizing the Expected Lifetime Spent in Drawdown Under Proportional Consumption (August 21, 2015). Finance Research Letters, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2649671

Bahman Angoshtari

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Virginia R. Young (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States
734-764-7227 (Phone)

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