  We solve the problem of mean-variance hedging for general semimartingale
models via stochastic control methods. After proving that the value process of
the associated stochastic control problem has a quadratic structure, we
characterize its three coefficient processes as solutions of semimartingale
backward stochastic differential equations and show how they can be used to
describe the optimal trading strategy for each conditional mean-variance
hedging problem. For comparison with the existing literature, we provide
alternative equivalent versions of the BSDEs and present a number of simple
examples.
