Paper: arXiv 2305.18136

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.

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 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.

Research Flowchart

  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"]