We analyze 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.

For the infinite investment horizon, we find that the optimal strategy coincides with the investment strategy that minimizes the probability of ruin, c.f. Young [North American Actuarial Journal, 8(4), 106-126, 2004] and Bauerle and Bayraktar [Stochastics, 86:2, 330-340, 2014]. However, this relationship does not necessarily hold if the investment horizon is not infinite. We show this by determining the optimal strategy for the lifetime problem (i.e. when the investment horizon is an exponential random variable) and assuming a constant rate of consumption. Speaker(s): Bahman Angoshtari (UM)