  In this work, we study the problem of mean-variance hedging with a random
horizon T ^ tau, where T is a deterministic constant and is a jump time of the
underlying asset price process. We rst formulate this problem as a stochastic
control problem and relate it to a system of BSDEs with jumps. We then provide
a veri cation theorem which gives the optimal strategy for the mean-variance
hedging using the solution of the previous system of BSDEs. Finally, we prove
that this system of BSDEs admits a solution via a decomposition approach coming
from ltration enlargement theory.
