We consider a hedger with a mean-variance objective who faces a random loss at a fixed time. The size of this loss depends quite generally on two correlated asset prices, while only one of them is available for hedging purposes. We present a simple solution of this hedging problem by introducing the intrinsic value process of a contingent claim.
"Mean-Variance Hedging for General Claims." Ann. Appl. Probab. 2 (1) 171 - 179, February, 1992. https://doi.org/10.1214/aoap/1177005776