Abstract: This paper uses the mean-variance model to study the portfolio selection problem with maximum drawdown constraint in the market environment with a finite number of states.First it points out that solution method to the model with risk-free asset is the same as the model without risk-free asset.Then it only studies the mean-variance of n kinds of risk securities with maximum drawdown constraint,obtains existence conditions and features of the mean-variance efficient frontier and boundary,and gives a specific solution method and procedure to obtain the explicit expression of efficient frontier and boundary of the model,Finally,as an application and a demonstration of these results,a numerical example.is given.

Key words: efficient frontier, maximum drawdown constraint, efficient constrain set, Kuhn-Tucker condition convex quadratic