Dynamic mean-variance portfolio selection with exogenous liability and borrowing constraint

In this paper, we consider a dynamic mean-variance model for asset and liability management with borrowing constraint. The purpose of this paper is to derive an optimal portfolio strategy and an efficient frontier. Since the problem can be formulated as a stochastic piecewise linear-quadratic (PLQ) control problem, we employ the Hamilton-Jacobi-Bellman (HJB) equation and the Lagrangian duality theory to solve this problem. A numerical example is given to demonstrate our results and show the impact of borrowing constraint on the efficient frontier.