  We study the pricing and the hedging of claim {\psi} which depends on the
default times of two firms A and B. In fact, we assume that, in the market, we
can not buy or sell any defaultable bond of the firm B but we can only trade
defaultable bond of the firm A. Our aim is then to find the best price and
hedging of {\psi} using only bond of the firm A. Hence, we solve this problem
in two cases: firstly in a Markov framework using indifference price and
solving a system of Hamilton-Jacobi-Bellman equations, secondly, in a more
general framework, using the mean variance hedging approach and solving
backward stochastic differential equations (BSDE).
