What if we knew what the future brings? Optimal investment for a frontrunner with price impact

TL;DR

This paper explores optimal investment strategies when investors have limited future knowledge and face quadratic transaction costs, providing explicit solutions using Gaussian Volterra integral equations.

Contribution

It introduces an explicit solution to a complex control problem with infinite-dimensional memory in a financial setting, leveraging duality and Gaussian Volterra equations.

Findings

Explicit solution to the control problem with future knowledge and transaction costs

Use of Gaussian Volterra integral equations to solve the dual problem

Insights into optimal investment strategies under partial future information

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.