Backward stochastic differential equations and stochastic controls

The paper attempts to explore the relationship between backward stochastic differential equations (BSDEs) and stochastic controls by interpreting a BSDE as some stochastic optimal control problem. The latter is solved in a closed form by the stochastic linear-quadratic (LQ) theory. The general result is then applied to the Black-Scholes model, where an optimal mean-variance hedging portfolio is obtained explicitly in terms of the option price. Finally, a modified model is investigated where the difference between the state and the expectation of the given terminal value at any time is taken into account