General indifference pricing with small transaction costs

We study the utility indifference price of a European option in the context of small transaction costs. Considering the general setup allowing consumption and a general utility function at final time T, we obtain an asymptotic expansion of the utility indifference price as a function of the asymptotic expansions of the utility maximization problems with and without the European contingent claim. We use the tools developed in [SIAM Journal on Control and Optimization 51 (2013), 28932921] and [Communications in Partial Differential Equations 40 (2015), 2005-2046] based on homogenization and viscosity solutions to characterize these expansions. Finally we study more precisely the example of exponential utilities, in particular recovering under weaker assumptions the results of [SIAM Journal on Financial Mathematics 3 (2012), 433-458].