What if we knew what the future brings, even on short term notice?

Abstract

We study optimal investment problems for an insider who can peek some time units into the future, but cannot arbitrarily 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 state variable. This is made possible by solving the dual problem where we make use of the theory of Gaussian Volterra integral equations. We also discuss a generalization of the model where the signal is perturbed by an independent Brownian noise. For the limiting case of very short term notice on price changes, we consider another model with jumps on which our investor receives a possibly noisy signal. Here dynamic programming allows us to compute an explicit optimal investment ratio which allows us to quantify the signal’s monetary value.

The first part of the talk is based on joint works with Yan Dolinsky and Miklos Rasonyi, the second is joint work with Laura Körber.