Open-loop equilibrium strategy for mean-variance asset-liability management with margin requirements

This paper considers a mean-variance asset-liability management problem in which short-selling is allowed, but accompanied by margin requirements. This is a mean-variance problem with a non linear state process. We derive a sufficient condition and a necessary condition for the time-consistent equilibrium strategy by using a system of forward backward stochastic differential equations. By decoupling this system, we obtain the unique equilibrium strategy. As a byproduct, we also get the equilibrium strategy for the mean-variance asset-liability management problem under short-selling prohibition.