Paper: arXiv 2610.20366

Authors: Karl Kristian Engelund

Abstract

Regime-switching multi-factor models are widely used in quantitative finance, but filtering does not by itself determine when an agent should act on inferred regime changes. We formulate online regime detection with latent factors and hidden regimes as a Bayesian decision problem balancing false alarms, detection delay, and misclassification. Since posterior regime probabilities are generally non-Markovian, the problem is represented as a measure-valued optimal stopping problem and approximated using particle filtering with Monte Carlo dynamic programming. A single-change-point Heston model provides a benchmark. With observed variance, the problem reduces to a two-dimensional Markov free-boundary problem, while under latent variance decisions are based on the filtered posterior measure. Numerical experiments in Heston and regime-switching Vasicek models show that the latent-information procedure can outperform feasible plug-in rules.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical and rigorous approach to a novel problem in quantitative finance. The combination of Bayesian decision theory, optimal stopping, and particle filtering is sophisticated, and the numerical experiments provide solid empirical backing for the proposed methodology. The work is well-structured and clearly articulated, making a significant contribution to the field.

Research Flowchart

  flowchart TD
    A[Research Goal: Online Regime Detection in Latent Factor Models] --> B{Methodology: Bayesian Decision Problem};
    B --> C[Approach: Measure-valued Optimal Stopping];
    C --> D{Approximation: Particle Filtering & Monte Carlo DP};
    D --> E[Models/Data: Heston, Vasicek, Latent Factors];
    E --> F[Outcomes: Outperformance of Latent-Information Procedure];