Mean-Variance Hedging and Stochastic Control: Beyond the Brownian Setting

We show for continuous semimartingales in a general filtration how the mean-variance hedging problem can be treated as a linear-quadratic stochastic control problem. The adjoint equations lead to backward stochastic differential equations for the three coefficients of the quadratic value process, and we give necessary and sufficient conditions for the solvability of these generalized stochastic Riccati equations. Motivated from mathematical finance, this paper takes a first step toward linear-quadratic stochastic control in more general than Brownian settings.