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

Asaf Cohen () and Yan Dolinsky ()
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Asaf Cohen: University of Michigan
Yan Dolinsky: Hebrew University

Finance and Stochastics, 2022, vol. 26, issue 2, No 6, 335-358

Abstract: 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 $n$ and when risk aversion is scaled like n ℓ $n\ell $ for some constant ℓ > 0 $\ell >0$ . 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.

Keywords: Utility indifference; Strong approximations; Path-dependent SDEs; Asymptotic analysis; 91G10; 60F15 (search for similar items in EconPapers)
JEL-codes: C65 G11 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00780-022-00473-y

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