In this paper we study optimal investment when the investor can peek some time units into the future, but cannot fully take advantage of this knowledge because of quadratic transaction costs. In the Bachelier setting with exponential utility, we give an explicit solution to this control problem with intrinsically infinite-dimensional memory. This is made possible by solving the dual problem where we make use of the theory of Gaussian Volterra integral equations.
Bibliographical noteFunding Information:
P. Bank is supported in part by the GIF Grant 1489-304.6/2019. Y. Dolinsky is supported in part by the GIF Grant 1489-304.6/2019 and the ISF Grant 230/21. M. Rásonyi thanks for the support of the “Lendület” Grant LP 2015-6 of the Hungarian Academy of Sciences.
© 2022, The Author(s).
- Exponential utility
- Gaussian Volterra integral equation
- Inside information
- Optimal investment
- Price impact