On Markowitz Geometrymath.OC
The paper explores Markowitz geometry in economics.
problem Mean-variance theory of efficient portfolios.
method Detailed treatment of Markowitz geometry.
result Solid mathematical foundation for portfolio theory.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Markowitz geometry”
The paper revisits Markowitz's pseudodistance on pseudo-Riemannian manifolds.
problem Characterizing and classifying pseudo-Riemannian manifolds using Markowitz's pseudodistance.
method Review and extension of Markowitz's construction of pseudodistance on pseudo-Riemannian manifolds, with examples and classifications.
result Classification of quasi-homogeneous domains in the Einstein-de Sitter space.
Study Gromov hyperbolic domains in Minkowski space, proving equivalence to boundary properties.
problem Investigate Gromov hyperbolic domains in Minkowski space.
method Explicit comparisons between metrics, dynamical arguments, and quasi-hyperbolic metric.
result Gromov hyperbolicity of convex, future complete domains is equivalent to stable acausality of the boundary.
The Markowitz Categoryq-fin.PM
Algebraic definition classifies Markowitz markets simplifying portfolio optimization.
problem Complexity in Markowitz market classification.
method Algebraic definition and isomorphism classification.
result Classification shows little beyond portfolio optimization insights.
Improved Markowitz method handles uncertainty in return forecasts.
problem Uncertainty in return statistics forecasts.
method Convex optimization with practical constraints.
result Handles uncertainty gracefully and efficiently.
Develops tests for Markowitz stochastic dominance spanning using saddle points.
problem Determining if adding securities or relaxing investment constraints improves investment opportunity sets.
method Derives properties of cdfs, defines Markowitz stochastic dominance spanning, constructs non-parametric tests based on subsampling.
result Rejects market portfolio Markowitz efficiency and finds evidence of outperformance.
A new portfolio optimization method using the Sherman-Morrison identity.
problem Portfolio optimization with covariance and variance.
method Sherman-Morrison identity applied to replace covariance with second moment matrix.
result Sherman-Morrison-Markowitz portfolio solves standard portfolio optimization problems.
Comparison of Markowitz Model and Single-Index Model on Portfolio Selection of Malaysian Stocksq-fin.PM
This study compares Markowitz and Single-Index models for Malaysian stocks.
problem Optimizing portfolio selection for Malaysian stocks using different models.
method Applied Markowitz and Single-Index models to 10-year historical data of 10 stocks and a risk-free asset.
result Comparison of minimum variance and maximum Sharpe portfolios for both models under various constraints.
Intraday trading strategy based on time series and machine learning for Chinese stock marketq-fin.TR
Article proposes a profitable intraday trading strategy for Chinese stocks.
problem Intraday trading opportunities in Chinese stock market.
method Markowitz optimization and Multilayer Perceptron (MLP) for stock price prediction.
result Validation of Markowitz portfolio optimization and MLP for intraday stock price prediction.
Markowitz simplified portfolio returns assuming constant trade volumes.
problem Understanding portfolio returns and variance in markets with variable trade volumes.
method Investor observes market trades, models portfolio as single security, derives portfolio return and variance.
result Markowitz's equation for portfolio returns and variance is a simplified approximation of real markets with constant trade volumes.
Robustifying Markowitzecon.EM
Robustifies Markowitz portfolios to reduce transaction costs and improve performance.
problem Markowitz portfolios are unreliable due to estimation errors and extreme weights.
method Projected gradient descent and robust statistics for stable weights and costs.
result Robustified Markowitz portfolios have lower turnover and maintain or improve performance.
We formalize causal separation in portfolio theory, deriving a closed-form projected Markowitz solution.
problem Portfolio optimization under causal separation conditions.
method Derive a closed-form solution for portfolio optimization using causal separation conditions.
result A closed-form projected Markowitz solution is derived under causal separation conditions.
Bayesian Markowitz portfolio problem shows entropy regularization is ineffective.
problem Entropy regularization in Bayesian Markowitz portfolio optimization.
method Combines continuous-time Bayesian filtering with stochastic policy optimization.
result Entropy regularization does not accelerate learning of unknown drift.
Solves portfolio optimization with cardinality constraints using column generation.
problem Portfolio optimization with cardinality constraints.
method Column generation method applied to a subset of assets in a master convex quadratic problem, using dual information to propose new assets.
result Solves portfolio optimization problems efficiently with cardinality constraints.
Improved portfolio optimization using machine learning and hierarchical clustering.
problem Suboptimal out-of-sample performance and unrealistic allocations in the Markowitz Model.
method Refined Markowitz Model with hierarchical clustering-based approach.
result Enhanced portfolio performance on a risk-adjusted basis.
Markowitz Meets Bellman: Knowledge-distilled Reinforcement Learning for Portfolio Managementq-fin.CP
Hybrid approach combines Markowitz's theory with reinforcement learning for optimal portfolio management.
problem Optimizing investment portfolios while balancing returns and risks.
method Knowledge distillation for training reinforcement learning agents.
result Achieves highest yield and Sharpe ratio of 2.03, ensuring top profitability with low risk.
Bayesian method improves portfolio selection by updating expected returns.
problem Optimizing portfolio selection with unknown expected returns.
method Bayesian filtering and dynamic programming for learning posterior distribution.
result Explicit optimal strategy computed for Gaussian prior, quantifying learning impact.
Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences-Stochastic Factor Caseq-fin.PM
We consider an incomplete market with a nontradable stochastic factor and a continuous time investment problem with an optimality criterion based on monotone mean-variance preferences. We formulate it as a stochastic differential game problem and use Hamilton-Jacobi-Bellman-Isaacs equations to find an optimal investmen…
Portfolio Analysis Based on Markowitz Stochastic Dominance Criteria: A Behavioral Perspectiveq-fin.PM
The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.
problem Understanding how behavioral investors make portfolio decisions.
method Developed stochastic optimization problems and MILP models to capture subjective decision weights and probability weighting functions.
result The developed models can be used to formulate computationally tractable portfolio analysis problems.
Multiscale Markowitzq-fin.PM
This paper improves traditional Markowitz optimization by considering variance at multiple time scales.
problem Traditional Markowitz optimization limits to a single time scale, ignoring variance across different frequencies.
method Introduces multifrequency optimization allowing specification of target Hurst exponents across multiple time scales.
result Effective risk management strategy that aligns with investor preferences at various time scales.
This paper shows Markowitz-style strategies are inefficient when considering drawdown risk.
problem Inefficiency of Markowitz-style investment strategies in recursive betting scenarios.
method Use of drawdown as risk metric, time-varying linear feedback block K(k) called the drawdown modulator.
result Classical Markowitz-style strategies are inefficient when considering drawdown risk.
The asymptotic distribution of the Markowitz portfolio is derived, for the general case (assuming fourth moments of returns exist), and for the case of multivariate normal returns. The derivation allows for inference which is robust to heteroskedasticity and autocorrelation of moments up to order four. As a side effect…
New method corrects Markowitz variance for trading volume fluctuations.
problem Incorrect risk estimates from Markowitz variance in trading environments.
method Modeling portfolio variance based on trade volume fluctuations.
result Market-based variance can significantly differ from Markowitz variance.
We briefly review the approach to optimization of portfolios according to the theory of Markowitz and propose a further modification that can improve the outcome of the optimization process. The modification takes account of the entropic contribution from the time series used to compute the parameters in the Markowitz …
Can robust optimization offer improved portfolio performance?: An empirical study of Indian marketq-fin.PM
Empirical study finds robust optimization can improve portfolio performance in Indian markets.
problem Comparing robust optimization to Markowitz model for portfolio performance.
method Three robust optimization models (box, ellipsoidal, separable uncertainty sets) tested on Indian market data.
result Robust optimization can be a viable alternative to Markowitz model in real market setups.
A new portfolio optimization model minimizes maximum drawdown, offering faster and more robust solutions.
problem Optimizing portfolios during financial distress, especially during crises.
method Linearization of Markowitz model based on maximum drawdown, with a Mixed-Integer Linear Programming variation.
result 200 times faster solving time with a more profitable and robust solution.
Naive Markowitz Policiesq-fin.MF
Naive investors make riskier choices than optimal strategies in continuous-time finance.
problem Continuous-time Markowitz portfolio selection with naive reoptimization.
method Analytical derivation of naive policies from discretely naive policies.
result Naive policies are always riskier and less efficient than equilibrium policies.
Paper tackles P vs NP problem in portfolio optimization with cardinality constraints and Black-Scholes derivatives.
problem Operationalizing the P vs NP problem in cardinality-constrained portfolio selection.
method Mixed-integer quadratic program with genetic algorithms, Monte Carlo sampling, and greedy screening.
result Cardinality constraint reshapes efficient frontier, highlighting trade-offs between stability and computational cost.
Study analyzes portfolio performance of crypto and traditional assets.
problem Impact of cryptocurrencies on portfolio performance.
method Used GARCH-Copula and GARCH-Vine Copula methods for risk structure calculation; Markowitz optimization for optimal asset weights.
result Portfolio with both crypto and traditional assets has higher Sharpe ratio and more stable performance.
New algorithm optimizes adaptive return level for Markowitz portfolios.
problem Finding an optimal return level for Markowitz portfolios when investor's risk appetite is unknown.
method Krasnoselskii-Mann Proximity Algorithm based on proximity operator and momentum technique.
result Significant improvements over state-of-the-art methods in portfolio optimization.
This paper optimizes portfolio selection for multivariate affine and quadratic Volterra models with rough volatilities.
problem Optimizing portfolio selection for multivariate models with rough volatilities and stochastic correlations.
method Investigates continuous-time Markowitz mean-variance problem for multivariate affine and quadratic Volterra models using Riccati backward stochastic differential equations (BSDEs).
result Derives explicit solutions for BSDEs in affine Volterra models and new analytic formulae for quadratic models.
This paper compares modern portfolio theories and applies them to real-world portfolio selection.
problem Balancing risk and return in financial investments.
method Introduction of Markowitz's MPT and Fernholz's SPT, application of four models (Markowitz, Constant Correlation, Single Index, Multi-Factor), and use of Portfolio Algorithm and time series models for prediction.
result Comparison and evaluation of portfolio performance and risk management strategies.
This paper bridges Markowitz planning and deep reinforcement learning for portfolio optimization.
problem Combining Markowitz planning and deep reinforcement learning for portfolio optimization.
method Mapping market conditions to actions using deep reinforcement learning, casting portfolio allocation as a continuous control problem.
result Deep reinforcement learning techniques can provide new insights for portfolio allocation.
Quantum computing optimizes ESG portfolios efficiently.
problem Optimizing investment portfolios with risk, return, and ESG considerations.
method Formulated discrete Markowitz portfolio theory (DMPT) for quantum annealers, incorporating ESG ratings.
result Discrete portfolios converge to continuous solutions as budgets increase, outperforming traditional methods.
Paper connects two portfolio methods, HRP and Minimum Variance, revealing their underlying similarity.
problem Inability to universally adopt optimization-based portfolio construction methods.
method Unifies Hierarchical Risk Parity and Minimum Variance approaches.
result Schur complementary allocation reveals the connection between HRP and Minimum Variance.
The main purpose of this study is the determination of the optimal length of the historical data for the estimation of statistical parameters in Markowitz Portfolio Optimization. We present a trading simulation using Markowitz method, for a portfolio consisting of foreign currency exchange rates and selected assets fro…
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimiz…
The paper describes a method to infer the signal-to-noise ratio in portfolio optimization.
problem Estimating the signal-to-noise ratio in portfolio optimization problems.
method A statistic similar to the Sharpe Ratio Information Criterion is used for inference.
result The method works well for reasonable sample and asset universe sizes.
ACGAN improves portfolio allocation by learning trends and uncertainty.
problem Markowitz framework's overemphasis on market uncertainty.
method Autoencoding CGAN (ACGAN) that learns trends and uncertainty.
result ACGAN leads to better portfolio allocation and more accurate series.
Paper solves portfolio selection under uncertain covariance matrix using robust optimization.
problem Optimizing portfolio selection under model uncertainty in covariance matrix.
method Formulates as a min-max mean-variance problem, solves using McKean-Vlasov dynamic programming.
result Provides explicit solutions for optimal robust portfolio strategies and robust efficient frontier.
HybridCGAN improves portfolio analysis by balancing trend prediction and market uncertainty.
problem Markowitz framework's overemphasis on market uncertainty and trend prediction.
method A hybrid approach combining deep generative models to balance trend prediction and market uncertainty.
result HybridCGAN leads to better portfolio allocation compared to existing methods.
New method solves portfolio optimization with cardinality constraints efficiently.
problem Real-world portfolio constraints like transaction costs and client preferences.
method Continuous relaxation method for NP-hard problems, extending Markowitz and CVaR models.
result Efficient algorithms find near-optimal portfolios for cardinality-constrained problems.
Signed network models reduce portfolio risk by considering negative edges in financial markets.
problem Tackles portfolio optimization in financial markets by exploiting negative edges in network representations.
method Proposes a discrete optimization scheme to reduce asset selection, building time series of signed networks from asset returns.
result Empirical results show that signed network portfolios perform similarly to classical mean-variance optimization and equally weighted benchmarks.
This note finds closed-form solutions for mean-risk portfolios using a specific type of mixture distribution.
problem Finding optimal portfolios under mean-risk criteria for general distributions.
method Using normal mean-variance mixture (NMVM) distributions, the paper derives closed-form expressions for mean-risk frontiers by optimizing a Markowitz model with adjusted return vectors.
result Closed-form solutions for mean-risk portfolios are found for return vectors following NMVM distributions.
New method solves stochastic control problems with delays using deep learning.
problem Stochastic control problems with delayed control in drift and diffusion.
method Characterization via Riccati PDEs and deep learning scheme.
result Illustrates effect of delay on Markowitz portfolio allocation problem.
Study on optimal portfolio selection with varying borrowing and saving rates in continuous-time markets.
problem Optimal portfolio selection in markets with different borrowing and saving rates.
method Hamilton-Jacobi-Bellman equation, partial differential equation, verification argument.
result Existence and smoothness of the value function, identification of trading regions and strategies.
Efficient Solution of Portfolio Optimization Problems via Dimension Reduction and Sparsificationq-fin.PM
Efficiently solves large portfolio optimization problems by reducing and sparsifying covariance matrices.
problem Large and dense covariance matrices limit efficient portfolio optimization.
method Dimension reduction and increased sparsity based on machine learning predictions.
result Improved portfolio performance and reduced runtime compared to full dense covariance matrices.
Given two families of continuous functions and on a topological space , we define a preorder on by the condition that any member of is an -increasing and any member of is an -decreasing function. It turns out that if the topological space is quasi-compact and sequentially com…