Exponential Utility Maximization in a Discrete Time Gaussian Framework

ArXiv ID: 2305.18136 “View on arXiv”

Authors: Unknown

Abstract

The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in Mathematical Finance, we also consider an investor who is informed about the risky asset’s price changes with a delay. Our method of solution is based on the theory developed in [“4”] and guessing the optimal portfolio.

Keywords: Utility Maximization, Exponential Utility, Multivariate Normal Distribution, Optimal Portfolio, Informational Delay

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats
• Why: The paper involves advanced mathematical concepts like matrix decompositions (banded matrices), probability measure theory, and non-Markovian optimization, but presents a theoretical solution with no backtesting, data, or implementation details.

  flowchart TD
    A["Research Goal<br>Exponential Utility Maximization<br>in Discrete Time Gaussian Framework"] --> B["Methodology<br>Theory from [4"] +<br>Optimal Portfolio Guessing]
    A --> C["Key Inputs<br>Multivariate Normal<br>Risky Asset +<br>Informational Delay"]
    B --> D["Computational Process<br>Solve HJB Equation &<br>Verify Optimality Conditions"]
    C --> D
    D --> E["Key Finding<br>Closed-form solution for<br>Optimal Portfolio Weights"]
    D --> F["Key Outcome<br>Explicit impact of<br>Informational Delay on Strategy"]