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

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...

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Bibliographic Details
Published in:Applied mathematics & optimization 2022-10, Vol.86 (2), Article 25
Main Authors: Bank, Peter, Dolinsky, Yan, Rásonyi, Miklós
Format: Article
Language:English
Subjects:
Applied mathematics
Calculus of Variations and Optimal Control
Optimization
Control
Cost control
Insider trading
Integral equations
Investment policy
Investments
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Simulation
Stochastic control theory
Systems Theory
Theoretical
Volterra integral equations
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Summary: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.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-022-09885-w