TY - JOUR

T1 - Short communication

T2 - A note on utility indifference pricing with delayed information

AU - Bank, Peter

AU - Dolinsky, Yan

N1 - Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Asymptotic analysis

KW - Hedging with delay

KW - Utility indifference pricing

UR - http://www.scopus.com/inward/record.url?scp=85105814202&partnerID=8YFLogxK

U2 - 10.1137/20m1379630

DO - 10.1137/20m1379630

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AN - SCOPUS:85105814202

SN - 1945-497X

VL - 12

SP - SC31-SC43

JO - SIAM Journal on Financial Mathematics

JF - SIAM Journal on Financial Mathematics

IS - 2

ER -