A Note on Utility Indifference Pricing with Delayed Information

TL;DR

This paper investigates utility indifference pricing in a delayed information setting within the Bachelier model, deriving a scaling limit that transforms the problem into a volatility control with quadratic penalty.

Contribution

It introduces a novel analysis of utility indifference prices under information delay, including a new scaling limit and a duality approach using relaxed martingale properties.

Findings

Derived a non-trivial scaling limit for vanishing delay

Formulated the problem as a volatility control with quadratic penalty

Extended duality techniques to delayed information settings

Abstract

We consider the Bachelier model with information delay where investment decisions can be based only on observations from $H>0$ time units before. Utility indifference prices are studied for vanilla options and we compute their non-trivial scaling limit for vanishing delay when risk aversion is scaled liked $A/H$ for some constant $A$. Using techniques from [7], we develop discrete-time duality for this setting and show how the relaxed form of martingale property introduced by [9] results in the scaling limit taking the form of a volatility control problem with quadratic penalty.