Mean-Variance Hedging via Stochastic Control and BSDEs for General Semimartingales

We solve the problem of mean-variance hedging for general semimartingale modelsvia stochastic control methods. After proving that the value process of theassociated stochastic control problem has a quadratic structure, we characteriseits three coefficient processes as solutions of semimartingale backward stochasticdifferential equations and show how they can be used to describe the optimaltrading strategy for each conditional mean-variance hedging problem. For comparisonwith the existing literature, we provide alternative equivalent versionsof the BSDEs and present a number of simple examples.[...]