Characterization of efficient frontier for mean-variance model with a drawdown constraint

This paper examines an optimal portfolio selection problem with a drawndown constraint based on mean-variance model when: (1) there is no arbitrage; (2) the market is complete; (3) there are finitely many states. First, we obtain the necessary and sufficient condition for the existence of the optimal solution to the problem. Then we prove that the efficient frontier of the model is a continuous and convex function, and the efficient frontier consists of a finite number of hyperbola segments and straight line segments with at most one subinterval corresponding to straight line segments. Moreover, we give some investment strategies by the results we obtained. Finally, we provide a numerical example to illustrate our results.