  Game contingent claims (GCCs) generalize American contingent claims by
allowing the writer to recall the option as long as it is not exercised, at the
price of paying some penalty. In incomplete markets, an appealing approach is
to analyze GCCs like their European and American counterparts by solving option
holder's and writer's optimal investment problems in the underlying securities.
By this, partial hedging opportunities are taken into account. We extend
results in the literature by solving the stochastic game corresponding to GCCs
with both continuous time stopping and trading. Namely, we construct Nash
equilibria by rewriting the game as a non-zero-sum stopping game in which
players compare payoffs in terms of their exponential utility indifference
values. As a by-product, we also obtain an existence result for the optimal
exercise time of an American claim under utility indifference valuation by
relating it to the corresponding nonlinear Snell envelope.
