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 nℓ for some constant ℓ> 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.
Bibliographical noteFunding Information:
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.
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
- Asymptotic analysis
- Path-dependent SDEs
- Strong approximations
- Utility indifference