What if We Knew What the Future Brings? Optimal Investment for a Frontrunner with Price Impact

Peter Bank; Yan Dolinsky; Miklós Rásonyi

doi:10.1007/s00245-022-09885-w

What if We Knew What the Future Brings? Optimal Investment for a Frontrunner with Price Impact

Peter Bank^*, Yan Dolinsky, Miklós Rásonyi

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	American English
Article number	25
Journal	Applied Mathematics and Optimization
Volume	86
Issue number	2
DOIs	https://doi.org/10.1007/s00245-022-09885-w
State	Published - Oct 2022

Bibliographical note

Funding 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.

Publisher Copyright:
© 2022, The Author(s).

Keywords

Exponential utility
Gaussian Volterra integral equation
Inside information
Optimal investment
Price impact

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10.1007/s00245-022-09885-w

Cite this

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abstract = "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.",

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N2 - 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.

AB - 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.

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KW - Gaussian Volterra integral equation

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KW - Price impact

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What if We Knew What the Future Brings? Optimal Investment for a Frontrunner with Price Impact

Abstract

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Keywords

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