Optimal investment with a noisy signal of future stock prices

Paper: arXiv 2302.10485

Authors: Peter Bank, Yan Dolinsky

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly sophisticated theoretical framework using stochastic control, partial observation, and convex duality to solve an optimal investment problem with price impact and asymmetric information. However, it is purely theoretical and completely lacks empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve optimal investment with dynamic noisy future price signal] --> B[Model Inputs: Independent Brownian motions, Exponential Utility & Temporary Price Impact]
    B --> C[Methodology: Formulate stochastic control problem with partial information]
    C --> D[Computational Step: Apply convex-analytic dual formulation]
    D --> E[Outcome: Closed-form solution for optimal trading strategy]
    D --> F[Outcome: Explicit value function under asymmetric information]