Minimizing the Probability of Lifetime Drawdown Under Constant Consumption

26 Pages Posted: 21 May 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: May 19, 2016

Abstract

We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following geometric Brownian motion as in the Black-Scholes model. Under a constant rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probability that her wealth drops below some fixed proportion of her maximum wealth to date, the so-called probability of lifetime drawdown. If maximum wealth is less than a particular value, m*, then the individual optimally invests in such a way that maximum wealth never increases above its current value. By contrast, if maximum wealth is greater than m* but less than the safe level, then the individual optimally allows the maximum to increase to the safe level.

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., Minimizing the Probability of Lifetime Drawdown Under Constant Consumption (May 19, 2016). Insurance: Mathematics and Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2781963

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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