Continuous-time Mean-variance Portfolio Selection With Margin Requirements

This paper is concerned with the continuous-time mean-variance portfolio selection with margin requirements. In this model, investor is required to deposit and maintain some amount of margin, the bank pays r(t) for any deposit, and takes R(t) for any loan. Convex duality method and backward stochastic differential equations is used to linearize the wealth equation, then introduce a Lagrange multiplier to convert the original problem to an unconstrained static optimum problem. At last, we obtain an equivalent optimum problem with convex domain. Specially, we calculate an example given r(t)=R(t).