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 asymptot...

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Bibliographic Details
Published inAsymptotic analysis Vol. 102; no. 3-4; pp. 177 - 226
Main Authors Possamaï, Dylan, Royer, Guillaume
Format Journal Article
LanguageEnglish
Published London, England SAGE Publications 01.01.2017
Sage Publications Ltd
IOS Press
Subjects
Asymptotic series
Mathematics
Partial differential equations
Probability
Utilities
homogenization
asymptotic expansions
viscosity solutions
Transaction costs
utility indifference pricing
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ISSN0921-7134
1875-8576
DOI10.3233/ASY-171415

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Summary: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].
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ISSN:0921-7134
1875-8576
DOI:10.3233/ASY-171415