Discrete time optimal investment under model uncertainty

ArXiv ID: 2307.11919 “View on arXiv”

Authors: Unknown

Abstract

We study a robust utility maximization problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real-line. She also faces model ambiguity on her beliefs about the market, which is modeled through a set of priors. We prove the existence of an optimal investment strategy using only primal methods. For that we assume classical assumptions on the market and on the random utility function as asymptotic elasticity constraints. Most of our other assumptions are stated on a prior-by-prior basis and correspond to generally accepted assumptions in the literature on markets without ambiguity. We also propose a general setting including utility functions with benchmark for which our assumptions are easily checked.

Keywords: robust utility maximization, quasi-sure no-arbitrage, model ambiguity, primal methods, asymptotic elasticity, General Financial Markets

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats
• Why: The paper is highly theoretical, featuring advanced stochastic analysis and measure theory without empirical validation or backtesting data, positioning it firmly in the theoretical ‘Lab Rats’ category.

  flowchart TD
    A["Research Goal: <br>Optimal Robust Utility Maximization <br>under Model Ambiguity"] --> B["Key Methodology: <br>Primal Methods (duality approach)"]
    B --> C["Inputs & Assumptions: <br>General Discrete-Time Market <br>Random Concave Utility <br>Set of Priors (Ambiguity)"]
    C --> D["Computational Process: <br>Existence of Optimal Strategy <br>Avoiding Quasi-Sure Arbitrage"]
    D --> E["Key Outcomes: <br>Existence Proof <br>Framework for Benchmark Utilities <br>Robust Strategy Solution"]