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 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.
Original language | English |
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Pages (from-to) | 335-358 |
Number of pages | 24 |
Journal | Finance and Stochastics |
Volume | 26 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2022 |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Keywords
- Asymptotic analysis
- Path-dependent SDEs
- Strong approximations
- Utility indifference