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Duality theory for exponential utility-based hedging in the Almgren–Chriss model

Part of: Mathematical finance Mathematical economics Stochastic analysis

Published online by Cambridge University Press:  03 August 2023

Yan Dolinsky
Yan Dolinsky*
Affiliation:
Hebrew University
*
*Postal address: Department of Statistics, Hebrew University, Jerusalem, Israel. Email address: yan.dolinsky@mail.huji.ac.il
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Abstract

In this paper we obtain a duality result for the exponential utility maximization problem where trading is subject to quadratic transaction costs and the investor is required to liquidate her position at the maturity date. As an application of the duality, we treat utility-based hedging in the Bachelier model. For European contingent claims with a quadratic payoff, we compute the optimal trading strategy explicitly.

Keywords

Exponential utilitydualitylinear price impactBachelier model

MSC classification

Primary: 91B16: Utility theory 91G10: Portfolio theory
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 2 , June 2024 , pp. 420 - 438
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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