## 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 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.

Original language | American English |
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Pages (from-to) | SC31-SC43 |

Journal | SIAM Journal on Financial Mathematics |

Volume | 12 |

Issue number | 2 |

DOIs | |

State | Published - 2021 |

### Bibliographical note

Publisher Copyright:© 2021 Society for Industrial and Applied Mathematics

## Keywords

- Asymptotic analysis
- Hedging with delay
- Utility indifference pricing