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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| Published in | Asymptotic analysis Vol. 102; no. 3-4; pp. 177 - 226 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
London, England
SAGE Publications
01.01.2017
Sage Publications Ltd IOS Press |
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| ISSN | 0921-7134 1875-8576 |
| DOI | 10.3233/ASY-171415 |
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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]. |
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| AbstractList | 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]. 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 [54] and [48] 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 [6]. |
| Author | Royer, Guillaume Possamaï, Dylan |
| Author_xml | – sequence: 1 givenname: Dylan surname: Possamaï fullname: Possamaï, Dylan organization: CMAP – sequence: 2 givenname: Guillaume surname: Royer fullname: Royer, Guillaume organization: CMAP |
| BackLink | https://hal.science/hal-01481367$$DView record in HAL |
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| Keywords | homogenization asymptotic expansions viscosity solutions Transaction costs utility indifference pricing |
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| Snippet | We study the utility indifference price of a European option in the context of small transaction costs. Considering the general setup allowing consumption and... |
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| SubjectTerms | Asymptotic series Mathematics Partial differential equations Probability Utilities |
| Title | General indifference pricing with small transaction costs |
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