A Scaling Limit for Utility Indifference Prices in the Discretized Bachelier Model

Asaf Cohen and Yan Dolinsky

Papers from arXiv.org

Abstract: We consider the discretized Bachelier model where hedging is done on an equidistant set of 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 get that the limiting problem takes the form of a volatility control problem.

Date: 2021-02, Revised 2022-03
New Economics Papers: this item is included in nep-upt
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