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A scaling limit for utility indifference prices in the discretised Bachelier model

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Abstract

We consider the discretised Bachelier model where hedging is done on a set of equidistant times. Exponential utility indifference prices are studied for path-dependent European options, and we compute their non-trivial scaling limit for a large number of trading times \(n\) and when risk aversion is scaled like \(n\ell \) for some constant \(\ell >0\). Our analysis is purely probabilistic. We first use a duality argument to transform the problem into an optimal drift control problem with a penalty term. We further use martingale techniques and strong invariance principles and obtain that the limiting problem takes the form of a volatility control problem.

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Acknowledgements

The authors thank the anonymous AE and reviewer for their valuable reports and comments which helped to improve the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Asaf Cohen

  2. Department of Statistics, Hebrew University, Jerusalem, Israel

    Yan Dolinsky

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  1. Asaf Cohen
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  2. Yan Dolinsky
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Correspondence to Yan Dolinsky.

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A. Cohen acknowledges the financial support of the National Science Foundation (DMS-2006305). Y. Dolinsky is supported in part by the GIF Grant 1489-304.6/2019 and the ISF grant 230/21.

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Cohen, A., Dolinsky, Y. A scaling limit for utility indifference prices in the discretised Bachelier model. Finance Stoch 26, 335–358 (2022). https://doi.org/10.1007/s00780-022-00473-y

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