Drawdown Controlled Optimal Portfolio Selection with Linear Constraints on Portfolio Weights

We solve the problem of constructing an optimal portfolio consisting of many risky assets to maximize the long-term growth rate of a representative agent's expected utility, subject to a set of general linear constraints on the portfolio weight vector as well as a constraint to prevent wealth drawdowns below a dynamic floor. The dynamic floor is defined as the time-decayed historical all-time high. Our results generalize those achieved by earlier authors, including Grossman and Zhou (1993) and Cvitannic and Karatzas (1994). Grossman and Zhou solved a special case of our problem by focusing on a single risky asset without portfolio weight constraints. Cvitanic and Karatzas solved a problem involving many risky assets but that ignored portfolio weight constraints and the time decay on the dynamic floor. To illustrate the usefulness of our method, we present several numerical examples based on both actual and simulated (Monte Carlo) returns. Finally, we suggest applications of our results to various practical investment management problems, including the management of hedge fund portfolios and 'principal-protected' investment strategies