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Optimal Investment to Minimize the Probability of Drawdown

Stochastics, Forthcoming

15 Pages Posted: 18 Feb 2016  

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: December 11, 2015

Abstract

We determine the optimal investment strategy in a Black-Scholes financial market to minimize the so-called probability of drawdown, namely, the probability that the value of an investment portfolio reaches some fixed proportion of its maximum value to date. We assume that the portfolio is subject to a payout that is a deterministic function of its value, as might be the case for an endowment fund paying at a specified rate, for example, at a constant rate or at a rate that is proportional to the fund's value.

Keywords: Optimal investment, stochastic optimal control, probability of drawdown

JEL Classification: C61, G02, G11

Suggested Citation

Angoshtari, Bahman and Bayraktar, Erhan and Young, V.R., Optimal Investment to Minimize the Probability of Drawdown (December 11, 2015). Stochastics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2732905

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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