Optimal investment with a noisy signal of future stock prices

TL;DR

This paper derives a closed-form solution for an optimal investment problem where an investor has noisy, dynamic information about future stock prices, accounting for temporary price impact and partial observation.

Contribution

It introduces a novel closed-form solution for a stochastic control problem with partial observation and temporary price impact, expanding understanding of optimal investment strategies under uncertainty.

Findings

Closed-form solution for the investment problem

Explicit characterization of the problem value

Effective handling of partial observation and price impact

Abstract

We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporary price impact the resulting optimal investment problem with exponential utility turns out to be not only well posed, but it even allows for a closed-form solution. We describe this solution and the resulting problem value for this stochastic control problem with partial observation by solving its convex-analytic dual problem.