Floating-Point Precision-Aware Differentiable Cardinality Constraint for Partial Index Tracking
- 주제(키워드) Constrained Optimization , Portfolio Optimization , Mathematical Approximation , Mathematical Optimization , XAI
- 주제(DDC) 006.31
- 발행기관 아주대학교 일반대학원
- 지도교수 Hyunsouk Cho
- 발행년도 2025
- 학위수여년월 2025. 2
- 학위명 석사
- 학과 및 전공 일반대학원 인공지능학과
- 실제URI http://www.dcollection.net/handler/ajou/000000034688
- 본문언어 영어
- 저작권 아주대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
Index tracking is a popular passive investment strategy aimed at optimizing portfolios, but fully replicating an index can lead to high transaction costs. To address this, partial replication have been proposed. However, the cardinality constraint renders the problem non-convex, non-differentiable, and often NP-hard, leading to the use of heuristic or neural network-based methods, which can be non-interpretable or have NP-hard complexity. To overcome these limitations, We propose a Differentiable Cardinality Constraint (DCC) for index tracking and introduce a floating-point precision-aware method (DCC_fpp) to address implementation issues. We theoretically prove our methods calculate cardinality accurately and enforce actual cardinality with polynomial time complexity, and we identify hyperparameter that ensure accurate results. Our method applied to mathematical method outperforms baseline methods across various datasets, demonstrating the effectiveness of the identified hyperparameter.
more목차
1 Introduction 1
1.1 Full and Partial Replication 1
1.2 Characteristics of cardinality Constraints 1
1.3 Proposal of the Differentiable cardinality Constraint (DCC) 2
2 Related Work 4
2.1 Mathematical Optimization for Full Replication 4
2.2 Heuristic Optimization for Partial Replication 5
2.3 Mathematical Optimization for Partial Replication 5
3 Preliminaries 6
3.1 Full Replication 6
3.2 Partial Replication 7
4 Differentiable Cardinality Constraint 9
4.1 Rational Function Approach 9
4.2 Sigmoid Function Approach (DCC_fpp) 11
4.2.1 Cardinality Constraint with Cutoff Threshold Consideration 11
4.2.2 Conditions for Accurate Cardinality Calculation 12
4.2.3 Conditions for Assurance of the DCC_fpp 12
4.2.4 Complex Analysis 15
5 Experiments 18
5.1 Experimental Settings 18
5.1.1 Data 18
5.1.2 Backtesting 19
5.1.3 Baselines 19
5.1.4 DCC_fpp 20
5.2 Index Tracking with Cardinality Constraint 20
5.3 Efficiency 22
5.4 Hyperparameter Analysis 24
6 Conclusion 26
Bibliography 27
