Paper: arXiv 2609.29887

Authors: Yi-Chen Liu, Chung-Han Hsieh

Abstract

This paper investigates cost-sensitive online window size selection for portfolio management under changing market conditions. Specifically, we propose a two-level framework that constructs portfolios using candidate window sizes and dynamically aggregates them through online learning. By treating candidate window sizes as ``experts,’’ we dynamically update their aggregation weights using turnover-inclusive losses. Moreover, we derive finite-horizon cost-sensitive tracking-regret bounds that account for turnover of the aggregated portfolio, with static regret as a special case. Under bounded losses and cost rates, suitably tuned Fixed Share achieves asymptotically no tracking regret for sublinear switching budgets, with Hedge covering the static case.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly mathematical framework for cost-sensitive online window selection with strong theoretical guarantees. While the theoretical rigor is high, the excerpt provided does not detail any empirical validation or backtesting, which is crucial for quant finance. The novelty lies in integrating turnover costs into regret bounds for dynamic window selection.

Research Flowchart

  flowchart TD
    A[Research Goal: Cost-Sensitive Online Window Size Selection for Portfolio Management] --> B{Key Methodology: Two-Level Framework};
    B -- Level 1: Portfolio Construction --> C[Candidate Window Sizes as "Experts"];
    B -- Level 2: Dynamic Aggregation --> D[Online Learning: Update Aggregation Weights with Turnover-Inclusive Losses];
    C & D --> E[Computational Process: Derive Finite-Horizon Cost-Sensitive Tracking-Regret Bounds];
    E --> F{Key Findings: Asymptotically No Tracking Regret (Fixed Share), Static Case Covered (Hedge)};