Short Communication: A Note on Utility Indifference Pricing with Delayed Information

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 nontrivial scaling limit for vanishing delay when risk aversion is scaled like $A/H$ for some constant $A$. Using techniques from [M. Fritelli, Math. Finance, 10 (2000), pp. 39--52], we develop discrete-time duality for this setting and show how the relaxed form of the martingale property introduced by [Y. Kabanov and C. Stricker, The Dalang--Morton--Willinger theorem under delayed and restricted information, in In Memoriam Paul-André Meyer: Séminaire de Probabilités XXXIX, Lecture Notes in Math. 1874, Springer, Berlin, 2006, pp. 209--213] results in the scaling limit taking the form of a volatility control problem with quadratic penalty.