Paper: arXiv 2409.13608

Abstract

Markowitz’s criterion aims to balance expected return and risk when optimizing the portfolio. The expected return level is usually fixed according to the risk appetite of an investor, then the risk is minimized at this fixed return level. However, the investor may not know which return level is suitable for her/him and the current financial circumstance. It motivates us to find a novel approach that adaptively optimizes this return level and the portfolio at the same time. It not only relieves the trouble of deciding the return level during an investment but also gets more adaptive to the ever-changing financial market than a subjective return level. In order to solve the new model, we propose an exact, convergent, and efficient Krasnoselskii-Mann Proximity Algorithm based on the proximity operator and Krasnoselskii-Mann momentum technique. Extensive experiments show that the proposed method achieves significant improvements over state-of-the-art methods in portfolio optimization. This finding may contribute a new perspective on the relationship between return and risk in portfolio optimization.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces advanced mathematics (proximity operators, Krasnoselskii-Mann momentum technique) to solve a non-trivial convex optimization problem, and it reports extensive experiments with performance metrics over state-of-the-art methods, making it both mathematically dense and empirically rigorous.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Adaptive Portfolio Optimization"] --> B["Key Inputs:<br>Asset Returns & Covariance Matrix"]
  B --> C["Methodology:<br>Krasnoselskii-Mann Proximity Algorithm"]
  C --> D["Computational Process:<br>Adaptive Return Level + Portfolio Weights"]
  D --> E["Key Finding:<br>Superior Risk-Return Trade-off"]

Cited References (105)

  1. Multi-period portfolio selection under the coherent fuzzy environment with dynamic risk-tolerance and expected-return levels (2022)
  2. A multi-period fuzzy portfolio optimization model with minimum transaction lots (2015)
  3. Reweighted price relative tracking system for automatic portfolio optimization (2020)
  4. Hyperspectral Image Classification via Discriminant G abor Ensemble Filter (2022)
  5. Convex analysis (1970)
  6. Signal recovery by proximal forward-backward splitting (2005)
  7. Quelques propri 'e t 'e s des op 'e rateurs angle-born 'e s etn-cycliquement monotones (1977)
  8. Fonctions convexes duales et points proximaux dans un espace hilbertien (1962)
and 97 more
  1. A Krasnoselskii-Mann Algorithm With an Improved EM Preconditioner for PET Image Reconstruction (2019)
  2. Proximity algorithms for image models: denoising (2011)
  3. Fast proximity-gradient algorithms for structured convex optimization problems (2016)
  4. Multi-step fixed-point proximity algorithms for solving a class of optimization problems arising from image processing (2015)
  5. Two remarks on the method of successive approximations (1955)
  6. Mean value methods in iteration (1953)
  7. Convex Analysis and Monotone Operator Theory in Hilbert Space (2017)
  8. Compositions and convex combinations of averaged nonexpansive operators (2015)
  9. Numerical Optimization (2006)
  10. Performance hypothesis testing with the S harpe ratio (2003)
  11. Performance Hypothesis Testing with the Sharpe and Treynor Measures (1981)
  12. Robust performance hypothesis testing with the Sharpe ratio (2008)
  13. Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem (2016)
  14. Real-world datasets for portfolio selection and solutions of some stochastic dominance portfolio models (2016)
  15. OR-Library: Distributing Test Problems by Electronic Mail (1990)
  16. ABCs of Trading: Behavioral Biases affect Stock Turnover and Value * (2015)
  17. Macroeconomic news, stock turnover, and volatility clustering in daily stock returns (2005)
  18. Heterogeneous turnover-performance relations (2021)
  19. A state-space modeling of the information content of trading volume (2019)
  20. Stock return predictability: Evidence from moving averages of trading volume (2021)
  21. Nonlinearity matters: The stock price – trading volume relation revisited (2021)
  22. Rights offerings in Spain: Effects on ex-rights stocks during the subscription period (2006)
  23. Ex-day behavior of japanese stock prices: New insights from new methodology (1990)
  24. Adjustment to Future Dividend Rates in the Prediction of Ex-rights Prices (1974)
  25. The impact of trading halts on liquidity and price volatility: Evidence from the Australian Stock Exchange (2011)
  26. Holding Back Volatility: Circuit Breakers, Price Limits, and Trading Halts (2013)
  27. The effects of trading suspensions in China (2019)
  28. Technical analysis and sentiment embeddings for market trend prediction (2019)
  29. Sentiment-aware volatility forecasting (2019)
  30. Long Short-Term Memory (1997)
  31. Computational Intelligence and Financial Markets: A Survey and Future Directions (2016)
  32. Random Forests (2001)
  33. Public Mood–Driven Asset Allocation: the Importance of Financial Sentiment in Portfolio Management (2018)
  34. Affective Computing and Sentiment Analysis (2016)
  35. The Properties of Equally Weighted Risk Contribution Portfolios (2010)
  36. Properties of the most diversified portfolio (2013)
  37. Portfolio Diversification (2017)
  38. Introduction to Risk Parity and Budgeting (2013)
  39. A Minimax Portfolio Selection Rule with Linear Programming Solution (1998)
  40. Reinforcement Learning in Continuous Time and Space (2000)
  41. Introduction to Probability Models (2014)
  42. Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework (2000)
  43. A Direct Estimation Approach to Sparse Linear Discriminant Analysis (2011)
  44. Safety-first dynamic portfolio selection (1998)
  45. On the Use of Mean-Variance and Quadratic Approximations in Implementing Dynamic Investment Strategies: A Comparison of Returns and Investment Policies (1993)
  46. An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs (1991)
  47. On the optimality of some multi-period selection criteria (1974)
  48. Optimal Multiperiod Portfolio Policies (1968)
  49. Computational aspects of minimizing conditional value-at-risk (2006)
  50. An enhanced model for portfolio choice with SSD criteria: a constructive approach (2011)
  51. Dual stochastic dominance and related mean-risk models (2002)
  52. Stochastic Dominance: An Approach to Decision-making Under Risk (1978)
  53. Enhanced indexation based on second-order stochastic dominance (2013)
  54. Size matters: Optimal calibration of shrinkage estimators for portfolio selection (2013)
  55. Portfolio selection models: a review and new directions (2009)
  56. Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets (1983)
  57. The capital asset pricing model (CAPM), short-sale restrictions and related issues (1977)
  58. The arbitrage theory of capital asset pricing (1976)
  59. High dimensional covariance matrix estimation using a factor model (2008)
  60. Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps (2003)
  61. On estimating the expected return on the market: An exploratory investigation (1980)
  62. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection (2003)
  63. Risk and asset allocation (2005)
  64. A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms (2009)
  65. Reinforcement Learning in Continuous Time and Space: A Stochastic Control Approach (2020)
  66. Continuous-time mean–variance portfolio selection: A reinforcement learning framework (2020)
  67. A linear programming model for selection of sparse high-dimensional multiperiod portfolios (2019)
  68. Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation (2000)
  69. 60 Years of portfolio optimization: Practical challenges and current trends (2014)
  70. Transaction cost optimization for online portfolio selection (2018)
  71. The Dow theory: an explanation of its development and an attempt to define its usefulness as an aid in speculation (1933)
  72. On-Line Portfolio Selection Using Multiplicative Updates (1998)
  73. New Support Vector Algorithms (2000)
  74. A Linear Classification Model Based on Conditional Geometric Score (2005)
  75. Robustness and sensitivity analysis of risk measurement procedures (2010)
  76. On the role of norm constraints in portfolio selection (2011)
  77. Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices (1995)
  78. Robust Asset Allocation (2004)
  79. Robust portfolio selection problems (2003)
  80. Bayes-Stein Estimation for Portfolio Analysis (1986)
  81. Stein's estimation rule and its competitors: an empirical B ayes approach (1973)
  82. A well-conditioned estimator for large-dimensional covariance matrices (2004)
  83. Optimization of conditional value-at-risk (2000)
  84. Approaching Mean-Variance Efficiency for Large Portfolios (2019)
  85. Machine Learning and Portfolio Optimization (2018)
  86. Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions (2015)
  87. Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy? (2009)
  88. Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets G oldilocks (2017)
  89. Calmar ratio: A smoother tool (1991)
  90. Maximum drawdown (2004)
  91. Value at Risk: The New Benchmark for Managing Financial Risk (1997)
  92. Riskmetrics technical document (1996)
  93. Portfolio Selection: Efficient Diversification of Investments (1959)
  94. Determinantal Rings (1988)
  95. Stochastic Portfolio Theory (2002)
  96. Universal Portfolios With and Without Transaction Costs (1999)
  97. Component-based face recognition with 3d morphable models

0 of 105 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.