Continuous-Time Path-Dependent Exploratory Mean-Variance Portfolio Construction

Paper: arXiv 2303.02298

Authors: Zhou Fang

Abstract

In this paper, we present an extended exploratory continuous-time mean-variance framework for portfolio management. Our strategy involves a new clustering method based on simulated annealing, which allows for more practical asset selection. Additionally, we consider past wealth evolution when constructing the mean-variance portfolio. We found that our strategy effectively learns from the past and performs well in practice.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 5.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a mathematically sophisticated continuous-time framework combining reinforcement learning concepts (exploratory formulation) with path-dependent mean-variance optimization. While the theoretical derivations and algorithmic structure via simulated annealing are strong, empirical validation is limited primarily to practical performance demonstrations rather than exhaustive multi-asset backtests.

Research Flowchart

  flowchart TD
    A[Research Goal: Continuous-Time Path-Dependent Exploratory Mean-Variance Strategy] --> B[Data Inputs: Equities Historical Price & Wealth Path Data]
    B --> C[Methodology Step 1: Simulated Annealing Asset Clustering]
    C --> D[Methodology Step 2: Reinforcement Learning & Path-Dependent Modeling]
    D --> E[Computational Process: Continuous-Time Portfolio Optimization]
    E --> F[Key Outcome: Strategy effectively learns from past wealth and performs well in practice]