Paper: arXiv 2408.07969
Authors: Yu Li, Yuhan Wu, Shuhua Zhang
Abstract
We study the continuous-time pre-commitment mean-variance portfolio selection in a time-varying financial market. By introducing two indexes which respectively express the average profitability of the risky asset (AP) and the current profitability of the risky asset (CP), the optimal portfolio selection is represented by AP and CP. Furthermore, instead of the traditional maximum likelihood estimation (MLE) of return rate and volatility of the risky asset, we estimate AP and CP with the second-order variation of an auxiliary wealth process. We prove that the estimations of AP and CP in this paper are more accurate than that in MLE. And, the portfolio selection is implemented in various simulated and real financial markets. Numerical studies confirm the superior performance of our portfolio selection with the estimation of AP and CP under various evaluation criteria.
Complexity vs Empirical Score
- Math Complexity: 7.5/10
- Empirical Rigor: 6.5/10
- Quadrant: Holy Grail — high math complexity, high empirical rigor
Why this score: The paper provides a rigorous mathematical derivation for continuous-time mean-variance portfolio selection using new indices (AP and CP) and second-order variation estimation rather than traditional MLE. It backs up these theoretical derivations with empirical evaluations across both simulated and real-world market datasets.
Research Flowchart
flowchart TD
A["Research Goal: Optimize continuous-time mean-variance portfolio in time-varying markets"] --> B["Data & Inputs: Simulated & real financial market asset prices"]
B --> C["Methodology: Introduce Average Profitability (AP) & Current Profitability (CP) indexes"]
C --> D["Computational Process: Estimate AP & CP via second-order variation of auxiliary wealth process"]
D --> E["Implementation: Execute pre-commitment portfolio strategy based on AP & CP"]
E --> F["Key Outcomes: More accurate parameter estimation than MLE & superior portfolio performance"]