Develops a new measure for market efficiency based on informational-entropy.
problem Lack of a precise quantitative definition of market efficiency.
method Develops a measure based on informational-entropy.
result The new measure is equivalent to existing definitions of market efficiency.
New divergences extend Bregman and skew Jensen, including f-divergences.
problem Developing new divergences to include f-divergences.
method Introducing g-Bregman and skew g-Jensen divergences, showing they include f-divergences.
result g-divergences generalize existing divergences and inequalities.
Study on geometric Jensen-Shannon divergence for Gaussian measures in Hilbert space.
problem Computing divergence between Gaussian measures in infinite-dimensional Hilbert space.
method Closed form expression and regularization for divergence calculation.
result Closed form expression and regularization for Geometric Jensen-Shannon divergence.
We present extensive evidence that ``risk premium'' is strongly correlated with tail-risk skewness but very little with volatility. We introduce a new, intuitive definition of skewness and elicit an approximately linear relation between the Sharpe ratio of various risk premium strategies (Equity, Fama-French, FX Carry,…
The submanifold quantum mechanics was opened by Jensen and Koppe (Ann. Phys. {\bf 63} (1971) 586-591) and has been studied for these three decades. This article gives its more algebraic definition and show what is the essential of the submanifold quantum mechanics from an algebraic viewpoint.
This study revisits Fama-French models using sample innovations to address misinterpretation of high R-squared values.
problem Misinterpretation of high R-squared values in Fama-French models due to serial dependence and volatility clustering.
method Use of sample innovations to derive standard econometrics time series models to overcome misinterpretation.
result Suggests the Fama-French model should consider heavy-tail distributions due to relevant tail behavior in financial data.
The paper tests stock return models and uses LSTM to predict stock returns.
problem Validating stock return models and predicting stock returns.
method Used Fama-French three-factor, four-factor, and five-factor models; also used LSTM model.
result Fama-French five-factor model shows better validity for stock returns.
We introduce various quantitative and mathematical definitions for price momentum of financial instruments. The price momentum is quantified with velocity and mass concepts originated from the momentum in physics. By using the physical momentum of price as a selection criterion, the weekly contrarian strategies are imp…
We propose a 4-factor model for overnight returns and give explicit definitions of our 4 factors. Long horizon fundamental factors such as value and growth lack predictive power for overnight (or similar short horizon) returns and are not included. All 4 factors are constructed based on intraday price and volume data a…
The paper examines the stability of Fama-French multi-factor models over time.
problem Stability of Fama-French multi-factor models over time.
method Rolling window method, Fama and MacBeth's two-step estimation, generalized GRS statistics.
result The effectiveness of Fama-French factors is not stable over time in all countries.
Jensen simplifies machine learning and optimization with an extensible toolkit.
problem Complex machine learning and optimization tasks in production environments.
method Develops a framework for convex functions and optimization algorithms, enabling easy deployment and extension.
result Jensen allows for quick model deployment and extension with minimal code, making machine learning accessible.
Proposes a new divergence measure for probability distributions.
problem Challenges in estimating divergences from empirical samples.
method Embeds data into RKHS, computes Jensen-Shannon divergence between covariance operators.
result Establishes RJSD as a lower bound on Jensen-Shannon divergence, enabling variational estimation.
New bound on machine learning model performance using Jensen-Shannon information.
problem Understanding the performance of machine learning models.
method Proposes a new information-theoretic bound on generalization error.
result Shows that the new bound can be tighter than mutual information-based bounds under certain conditions.
New framework using Jensen-Shannon divergence improves domain adaptation theory.
problem Incoherence between empirical domain adversarial training and theoretical H-divergence. method Established new theoretical framework based on Jensen-Shannon divergence, derived bi-directional upper bounds.
result Framework exhibits flexibilities for various transfer learning problems.
The Capital Asset Pricing Model (CAPM) is one of the original models in explaining risk-return relationship in the financial market. However, when applying the CAPM into reality, it demonstrates a lot of shortcomings. While improving the performance of the model, many studies, on one hand, have attempted to apply diffe…
A new objective function using Jensen-Shannon divergence improves generative learning from multiple data types.
problem Learning from multiple data types efficiently and accurately.
method Proposes a novel objective function using Jensen-Shannon divergence to approximate multimodal posteriors directly.
result The mmJSD objective optimizes an ELBO and improves generative learning tasks.
Proposes a new loss function for learning with noisy labels.
problem Improving model learnability with noisy labels.
method Uses generalized Jensen-Shannon divergence as a noise-robust loss function.
result Shows state-of-the-art results on noisy data.
Paper shows how to break down a specific type of divergence into simpler parts.
problem Understanding and simplifying divergence functions.
method Decomposes the symmetric Bregman divergence into two types of Jensen divergences and a Bregman divergence, and extends this to include f-divergences.
result Sum decomposition of divergence into simpler parts is possible.
In this report, we derive a non-negative series expansion for the Jensen-Shannon divergence (JSD) between two probability distributions. This series expansion is shown to be useful for numerical calculations of the JSD, when the probability distributions are nearly equal, and for which, consequently, small numerical er…
Study assesses additional factors for identifying persistent alpha in pension funds.
problem Identify persistent alpha in pension funds using additional factors.
method Reproduces Fama and French's (2010) experiment with additional features and compares results to 3-factor model.
result Additional factors improve persistence of alpha assessment in pension funds.
Study tests if equity factors explain Bitcoin's risk and returns.
problem Explaining Bitcoin's risk and return with equity factors.
method Applied statistical methods to test Fama-French factors on Bitcoin's excess returns.
result Fama-French factors have explanatory power on Bitcoin's risk and returns.
Develops LSH schemes for f-divergences and mutual information loss.
problem Approximating nearest neighbors in high-dimensional probability distributions.
method General framework and specific LSH schemes for f-divergences and mutual information loss.
result Generalized Jensen-Shannon divergence can be approximated by Hellinger distance.
Intangible investment becomes a strong predictor of stock returns over time.
problem Understanding the role of intangible investment in stock returns over different periods.
method Comparing intangible investment's predictive power over two distinct periods (1963-1992 and 1993-2022) using orthogonal factors.
result Intangible investment's predictive power for stock returns has significantly increased over time, becoming a main predictor for recent periods.
Study compares statistical properties and power of divergence measures for credit risk monitoring.
problem Detecting distributional shifts in credit risk models.
method Derives statistical properties and chi-square benchmark values for Jensen-Shannon Divergence and Kullback-Leibler Divergence, demonstrating their applicability in credit risk monitoring.
result Jensen-Shannon Divergence and Kullback-Leibler Divergence follow chi-square distributions and reveal practical trade-offs in minimizing false positives vs. detecting changes.
Study analyzes Disney stock market performance using machine learning.
problem Forecasting stock market performance of Disney.
method Exploratory data analysis, feature engineering, model selection (linear regression).
result Linear regression model performed best.
Empirical study of CAPM and Fama-French model in Chinese A-share market.
problem Testing and validating CAPM and Fama-French model in Chinese A-share market.
method Used Fama-MacBeth regression and Fama-French three-factor model to analyze Chinese A-share trading data from 2000 to 2019, adjusting for IPO shell value contamination.
result Fama-French model captures most of A-share market returns, with adjusted R-squared > 0.88.
New method improves understanding of machine learning model performance.
problem Understanding how well machine learning models generalize from training data to unseen data.
method Auxiliary Distribution Method to derive new generalization error bounds.
result Upper bounds on generalization errors are tighter and more applicable.
The paper explores how GANs' learned distribution aligns with real data distribution.
problem Aligning GAN's learned distribution with real data distribution.
method Optimizing Jensen-Shannon divergence to force alignment, comparing gradients of different distances.
result Wasserstein W22 may have desirable properties like reduced mode collapse. This paper investigates the common intuition suggesting that during crises the shape of the financial market clearly differentiates from that of random walk processes. In this sense, it challenges the analysis of the nature of financial markets proposed by Fama and his associates. For this, a geometric approach is prop…
We find that the CAPM fails to explain the small firm effect even if its non-parametric form is used which allows time-varying risk and non-linearity in the pricing function. Furthermore, the linearity of the CAPM can be rejected, thus the widely used risk and performance measures, the beta and the alpha, are biased an…
Proposes a new method for fairness in machine learning with multiple protected attributes.
problem Ensuring fairness in machine learning models with continuous and multiple protected attributes.
method Distance covariance regularisation framework to mitigate association between model predictions and protected attributes.
result Demonstrates effectiveness in mitigating fairness gerrymandering in regression tasks.
Study examines stock price reactions to Texas winter storm power outages.
problem Impact of natural disasters on stock market values.
method Used four benchmark models to measure abnormal returns.
result Firms experienced significant stock price drops after the Texas winter storm.
The paper proves a Jensen's inequality in spaces with lower bounded curvature.
problem Proving Jensen's inequality in geodesic spaces with curvature constraints.
method Using properties of tangent cones and gradients for semi-concave functions in spaces with lower bounded curvature.
result The inequality holds for geodesically convex functions in spaces with curvature lower bounded.
In the paper we give necessary and sufficient conditions for the Jensen inequality to hold for the generalized Choquet integral with respect to a pair of capacities. Next, we apply obtained result to the theory of risk aversion by providing the assumptions on utility function and capacities under which an agent is risk…
The paper analyzes financial market turbulence using mathematical physics.
problem Understanding price fluctuations caused by information asymmetry.
method Spectrum analysis to decompose pricing patterns.
result Identifies phase correlations in financial stock market turbulence.
A new metric uses nonparametric comparison for fitting parametric distributions.
problem Measuring goodness-of-fit for nonlinear models using maximum likelihood estimation.
method Survival Jensen-Shannon divergence (SJS) and its empirical counterpart (ESJS) for nonparametric comparison. result The ESJS can be used as a measure of goodness-of-fit in maximum likelihood estimation. Mathematical study of excess growth rate connects info theory with finance.
problem Understanding the excess growth rate in portfolio theory.
method Axiomatic characterization theorems of excess growth rate in terms of relative entropy, Jensen's inequality gap, and logarithmic divergence.
result Established rich connections between information theory and finance.
Study finds stock selection ability of Chinese mutual funds is better than asset allocation ability.
problem Evaluating the performance of actively managed mutual funds in China.
method Developed performance measures for asset allocation and selection using holding-based models and compared them with Fama-French and Treynor-Mazuy models.
result Stock selection ability from holding-based models is positively correlated with Fama-French model, while industry allocation is positively correlated with Treynor-Mazuy model.
Paper improves particle variational inference by optimizing generalization error bound.
problem Improving the diversity of models in particle variational inference to enhance generalization.
method Develops a new second-order Jensen inequality with a repulsion term based on the loss function, leading to a tighter generalization error bound.
result The proposed PVI optimizes the generalization error bound directly, improving performance compared to existing methods.
Extends online learning to metric spaces using exponential weights.
problem Online learning in metric spaces.
method Exponentially weighted average forecaster, barycenters, Jensen's inequality, measure contraction property.
result Results in a statistical learning framework.
The paper introduces a new divergence measure for variational autoencoders to improve reconstruction and generation.
problem Balancing reconstruction and generalizability in latent space of variational autoencoders.
method Presented a regularisation mechanism based on skew-geometric Jensen-Shannon divergence.
result The skew-geometric Jensen-Shannon divergence leads to better reconstruction and generation in variational autoencoders.
Paper defines conditions for feasible correlation matrices from factor structures.
problem Feasibility of option implied correlation matrices in non-FX markets.
method Quantitative and economic approaches to solve the nearest correlation matrix problem.
result Introduces methods to ensure feasible correlation matrices from factor structures.
Paper analyzes systematic jump risk around the clock using news narratives.
problem Identifying and managing priced risks in real-time market conditions.
method Combining high-frequency market data with news narratives classified by an LLM.
result Significant heterogeneity in risk premia, with macroeconomic news commanding the largest premium.
The study addresses overlooked data-generating processes in time-series asset pricing.
problem The literature on time-series asset pricing overlooks the data-generating processes for factors expressed in return differences.
method The study proposes a new definition of returns and compound returns for factors, and uses OLS with net returns for single-index models.
result OLS with net returns for single-index models leads to inflated alphas, exaggerated t-values, and overestimated Sharpe ratios.
Customer momentum is a positive relationship between a firm's returns and past returns of its customers.
problem Understanding the relationship between a firm's returns and its customers' past returns.
method Examined customer momentum using a long-short equally-weighted decile portfolio and Fama-French factor models.
result Customer momentum generates significant monthly returns and is statistically significant.
Method clusters molecular systems based on dynamics or structure similarity.
problem Clustering molecular systems based on dynamics or structure similarity.
method Ward's minimum variance clustering using Jensen-Shannon divergence.
result Method avoids overfitting in supervised learning.
Paper proposes new metrics to compare asset pricing models, incorporating Bayesian insights.
problem Power problems of statistical tests and misuse of alpha-based statistics.
method Unified set of distance-based performance metrics derived from alphas and standard errors, Bayesian interpretation of model performance.
result Bayesian approach favors models with low alpha dispersion and high explanatory power, especially the momentum factor.
We consider invariant Einstein metrics on the Stiefel manifold $V_q\bb{R} ^n$ of all orthonormal q-frames in $\bb{R}^n$. This manifold is diffeomorphic to the homogeneous space $\SO(n)/\SO(n-q)$ and its isotropy representation contains equivalent summands. %This causes difficulty in the description of all $\SO(n)$-in…