Option Pricing via Utility Maximization in the presence of Transaction Costs: an Asymptotic Analysis

We consider a multivariate financial market with proportional transaction costs as in Kabanov (1999). We study the problem of contingent claim pricing via utility maximization as in Hodges and Neuberger (1989). Using an exponential utility function, we derive a closed form characterization for the asymptotic price as the risk aversion tends to infinity. We prove that it is reduced to the super-replication cost if the initial endowment is only invested in the non-risky asset, as it was conjectured in Barles and Soner (1996). We do not make use of the dual formulation for the super-replication price obtained in Kabanov (1999).