We consider the Bachelier model with linear price impact. Exponential utility indifference prices are studied for vanilla European options, and we compute their nontrivial scaling limit for a vanishing price impact which is inversely proportional to the risk aversion. Moreover, we find explicitly a family of portfolios which are asymptotically optimal.
Bibliographical noteFunding Information:
\ast Received by the editors November 1, 2021; accepted for publication (in revised form) January 5, 2022; published electronically March 7, 2022. https://doi.org/10.1137/21M1456431 Funding: This work was supported by GIF grant 1489-304.6/2019 and by ISF grant 230/21. \dagger Department of Statistics, Hebrew University of Jerusalem, Jerusalem, 91905, Israel (email@example.com, firstname.lastname@example.org).
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- asymptotic analysis
- linear price impact
- utility indifference pricing