Paper: arXiv 2610.08631

Authors: Balazs Hoffmann, Miklos Rasonyi

Abstract

We investigate a continuous-time financial market where the asset price exhibits weak (sublinear) mean reversion and has a nonzero drift. Complementing earlier work on strong (superlinear) mean reversion, we show that, for an investor maximizing expected exponential utility, the certainty equivalent grows as $O(T^{2β+1})$ where $0<β<1$ is the strength of mean reversion. An explicit asymptotically optimal strategy is also given.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper is highly theoretical, focusing on advanced stochastic calculus and utility maximization. While it extends previous work with a novel approach to weak mean reversion, it lacks any empirical validation or data analysis. The mathematical derivations are rigorous and detailed.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Investment with Weak Mean Reversion] --> B(Methodology: Continuous-Time Financial Market Model);
    B --> C{Inputs: Asset Price Dynamics, Exponential Utility};
    C --> D[Computational Process: Solve Optimization Problem];
    D --> E(Key Finding 1: Certainty Equivalent Growth $O(T^{2β+1})$);
    E --> F[Key Finding 2: Explicit Asymptotically Optimal Strategy];