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Markowitz mean-variance portfolios with sample mean and covariance as input parameters feature numerous issues in practice. They perform poorly out of sample due to estimation error, they experience extreme weights together with high…

Econometrics · Economics 2022-12-29 Wolfgang Karl Härdle , Yegor Klochkov , Alla Petukhina , Nikita Zhivotovskiy

We propose a novel asset allocation model using a Markov process of states defined by clustered efficient frontier coefficients. While most research in Markov models of the market characterize regimes using return and volatility, we instead…

Portfolio Management · Quantitative Finance 2026-04-07 Nolan Alexander , William Scherer , Jamey Thompson

Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the…

Machine Learning · Computer Science 2024-05-28 Yu-Jie Zhang , Zhen-Yu Zhang , Peng Zhao , Masashi Sugiyama

Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of selected portfolios among a vast pool of assets, as demonstrated in Fan et al (2008). The required high-dimensional…

Portfolio Management · Quantitative Finance 2010-04-29 Jianqing Fan , Yingying Li , Ke Yu

Fixed income has received far less attention than equity portfolio optimisation since Markowitz' original work of 1952, partly as a result of the need to model rates and credit risk. We argue that the shape of the efficient frontier is…

Mathematical Finance · Quantitative Finance 2020-04-07 Richard J. Martin

More than seventy years ago Harry Markowitz formulated portfolio construction as an optimization problem that trades off expected return and risk, defined as the standard deviation of the portfolio returns. Since then the method has been…

Portfolio Management · Quantitative Finance 2024-01-11 Stephen Boyd , Kasper Johansson , Ronald Kahn , Philipp Schiele , Thomas Schmelzer

Markowitz (1952, 1959) laid down the ground-breaking work on the mean-variance analysis. Under his framework, the theoretical optimal allocation vector can be very different from the estimated one for large portfolios due to the intrinsic…

Portfolio Management · Quantitative Finance 2008-12-16 Jianqing Fan , Jingjin Zhang , Ke Yu

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…

Optimization and Control · Mathematics 2025-01-28 Arjun Ramachandra , Napat Rujeerapaiboon , Melvyn Sim

We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing Jeffreys' non-informative prior and the conjugate informative prior, we derive stochastic representations for the…

Statistics Theory · Mathematics 2023-04-19 David Bauder , Taras Bodnar , Nestor Parolya , Wolfgang Schmid

Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…

Machine Learning · Statistics 2020-06-26 Song Liu , Yulong Zhang , Mingxuan Yi , Mladen Kolar

In this paper, we tackle the dynamic mean-variance portfolio selection problem in a {\it model-free} manner, based on (generative) diffusion models. We propose using data sampled from the real model $\mathbb P$ (which is unknown) with…

Portfolio Management · Quantitative Finance 2025-09-03 Ahmad Aghapour , Erhan Bayraktar , Fengyi Yuan

Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two dimensional space…

Portfolio Management · Quantitative Finance 2018-05-16 Stanislaus Maier-Paape , Qiji Jim Zhu

This paper describes a method to estimate a production frontier that satisfies the axioms of monotonicity and concavity in a non-parametric Bayesian setting. An inefficiency term that allows for significant departure from prior…

Methodology · Statistics 2015-10-08 José Luis Preciado Arreola , Andrew L. Johnson

In performative prediction, predictions guide decision-making and hence can influence the distribution of future data. To date, work on performative prediction has focused on finding performatively stable models, which are the fixed points…

Machine Learning · Computer Science 2021-06-17 John Miller , Juan C. Perdomo , Tijana Zrnic

Early-exiting neural networks enable adaptive inference by allowing inputs to exit at intermediate classifiers, reducing computation for easy samples while maintaining high accuracy. In practice, exits can be trained sequentially by…

Machine Learning · Computer Science 2026-05-08 Alaa Zniber , Ouassim Karrakchou , Mounir Ghogho

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.…

Portfolio Management · Quantitative Finance 2024-11-08 Yizun Lin , Yongxin He , Zhao-Rong Lai

Optimizing portfolio performance is a fundamental challenge in financial modeling, requiring the integration of advanced clustering techniques and data-driven optimization strategies. This paper introduces a comparative backtesting approach…

Machine Learning · Computer Science 2025-01-23 Keon Vin Park

We consider the problem of selecting a portfolio of assets that provides the investor a suitable balance of expected return and risk. With respect to the seminal mean-variance model of Markowitz, we consider additional constraints on the…

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 Andrea Schaerf

Stock price prediction is a challenging task and a lot of propositions exist in the literature in this area. Portfolio construction is a process of choosing a group of stocks and investing in them optimally to maximize the return while…

Portfolio Management · Quantitative Finance 2022-01-17 Jaydip Sen , Ashwin Kumar R S , Geetha Joseph , Kaushik Muthukrishnan , Koushik Tulasi , Praveen Varukolu

Markowitz's celebrated mean--variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the…

Applications · Statistics 2011-08-05 Tze Leung Lai , Haipeng Xing , Zehao Chen