Paper: arXiv 2506.07299

Authors: Hans Buehler, Blanka Horvath, Yannick Limmer, Thorsten Schmidt

Abstract

This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the unavailability of the true probability measure forces reliance on an empirical approximation, and even small misestimations can lead to significant deviations in decision quality. Building on the framework of Klibanoff et al. (2005), we enhance the conventional objective - whether this is expected utility in an investing context or a hedging metric - by superimposing an outer “uncertainty measure”, motivated by traditional monetary risk measures, on the space of models. In scenarios where a natural model distribution is lacking or Bayesian methods are impractical, we propose an ad hoc subsampling strategy, analogous to bootstrapping in statistical finance and related to mini-batch sampling in deep learning, to approximate model uncertainty. To address the quadratic memory demands of naive implementations, we also present an adapted stochastic gradient descent algorithm that enables efficient parallelization. Through analytical, simulated, and empirical studies - including multi-period, real data and high-dimensional examples - we demonstrate that uncertainty measures outperform traditional mixture of measures strategies and our model-agnostic subsampling-based approach not only enhances robustness against model risk but also achieves performance comparable to more elaborate Bayesian methods.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.2/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a mathematical framework with formal definitions of uncertainty measures and optimisation, requiring knowledge of stochastic calculus and risk measures, while also providing empirical validation through simulation, real data, and algorithmic implementation.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Address Model Uncertainty<br>in Financial Optimization"] --> B["Framework Enhancement<br>Uncertainty-Aware Objective<br>Based on Klibanoff et al."]
  B --> C["Proposed Methodology<br>Model-Agnostic Subsampling<br>to Approximate Uncertainty"]
  C --> D["Computational Process<br>Adapted Stochastic Gradient Descent<br>for Efficiency & Parallelization"]
  D --> E["Data/Inputs<br>Analytical, Simulated,<br>Multi-period Real Data"]
  E --> F["Key Outcomes & Findings<br>Robustness against model risk<br>Comparable to Bayesian methods<br>Superior to mixture strategies"]

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2 of 89 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.