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Abstract

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), 2893–2921] 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].

Keywords

Transaction costs homogenization viscosity solutions utility indifference pricing asymptotic expansions

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General indifference pricing with small transaction costs

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