Paper: arXiv 2212.07516

Authors: Lin Chen, Xun Yu Zhou

Abstract

We study a continuous-time Markowitz mean-variance portfolio selection model in which a naive agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naive policies through the limit of discretely naive policies that are committed only in very small time intervals, and derive them analytically and explicitly. We compare naive policies with pre-committed optimal policies and with consistent planners’ equilibrium policies in a Black-Scholes market, and find that the former are mean-variance inefficient starting from any given time and wealth, and always take riskier exposure than equilibrium policies.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical analysis of continuous-time mean-variance optimization with time-inconsistent naive agents, delivering clear analytical and explicit policy derivations. However, it is purely theoretical and lacks empirical backtesting or real-world market data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Analyze Naive Policies in Continuous-Time Markowitz Selection"] --> B["Market Inputs: Black-Scholes Model & Mean-Variance Criteria"]
    B --> C["Methodology: Formulate Discretely Naive Policies with Short Commitments"]
    C --> D["Computational Process: Derive Continuous-Time Limit via Analytical Solving"]
    D --> E["Comparison: Benchmark Naive vs. Pre-Committed vs. Equilibrium Policies"]
    E --> F["Key Outcomes: Naive Policies are Inefficient & Consistently Riskier Than Equilibrium"]