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

Asaf Cohen, Yan Dolinsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageAmerican English
Pages (from-to)335-358
Number of pages24
JournalFinance and Stochastics
Volume26
Issue number2
DOIs
StatePublished - 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

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