Optimal Investment to Minimize the Probability of Drawdown
arXiv:1506.00166
Abstract
We determine the optimal investment strategy in a Black-Scholes financial market to minimize the so-called {\it 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.
arXiv commentTo appear in Stochastics. Keywords: Optimal investment, stochastic optimal control, probability of drawdown