Exponential Utility Maximization with Delay in a Continuous Time Gaussian Framework

Paper: arXiv 2311.17270

Authors: Yan Dolinsky

Abstract

In this work we study the continuous time exponential utility maximization problem in the framework of an investor who is informed about the price changes with a delay. This leads to a non-Markovian stochastic control problem. In the case where the risky asset is given by a Gaussian process (with some additional properties) we establish a solution for the optimal control and the corresponding value. Our approach is purely probabilistic and is based on the theory for Radon-Nikodym derivatives of Gaussian measures developed by Shepp [6] and Hitsuda [5].

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using advanced probabilistic tools (Radon-Nikodym derivatives of Gaussian measures) to solve a non-Markovian stochastic control problem with delayed information. However, it is a purely theoretical paper with no empirical validation or backtesting on real-market data.

Research Flowchart

  flowchart TD
    A[Goal: Exponential Utility Maximization with Delayed Information] --> B[Inputs: Risky Asset as Gaussian Process & Delayed Price Signals]
    B --> C[Formulate Non-Markovian Stochastic Control Problem]
    C --> D[Apply Shepp & Hitsuda Theory on Radon-Nikodym Derivatives]
    D --> E[Probabilistic Derivation of Optimal Control Strategy]
    E --> F[Outcomes: Explicit Solution for Optimal Control & Value Function]