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We price a contingent claim liability using the utility indifferenceargument. We consider an agent with exponential utility, who invests in a stockand a money market account with the goal of maximizing the utility of hisinvestment at the final time T in the presence of positive proportionaltransaction cost in two cases with and without a contingent claim liability.Using the computations from the heuristic argument in Whalley & Wilmott weprovide a rigorous derivation of the asymptotic expansion of the value functionin powers of the transaction cost parameter around the known value function forthe case of zero transaction cost in both cases with and without a contingentclaim liability. Additionally, using utility indifference method we derive anasymptotic expansion of the price of the contingent claim liability. In bothcases, we also obtain a "nearly optimal" strategy, whose expected utilityasymptotically matches the leading terms of the value function.

Pricing a Contingent Claim Liability with Transaction Costs Using Asymptotic Analysis for Optimal Investment