arXiv research

This work presents a parametrized family of divergences, namely Alpha-Beta Log- Determinant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infi…

The paper develops divergences for Gaussian processes and RKHS settings.

The study examines averages of Laplacian determinants over large genus moduli spaces.

DAGMA learns DAGs faster and more accurately using log-determinant acyclicity.

Local index theorem for cofinite hyperbolic Riemann surfaces derived from computational perspective.

For a smooth strictly plurisubharmonic function $u$ on a open set $Ω\subset\mathbb{C}^{n}$ and $F$ a $C^{1}$ nondecreasing function on $\mathbf{R}^{*}_{+}$, we investigate the complex partial differential equations $Δ_{g}\log\det(u_{i\bar j})=F(\det(u_{i\bar j}))\Vert\nabla_{g}\log\det(u_{i\bar j})\Vert_{g}^{2},$ whe…

Alpha2 discovers logical formulaic alphas using deep reinforcement learning.

Alpha-GPT mines new trading signals with human-AI interaction.

We give an explicit algorithm and source code for extracting expected returns for stocks from expected returns for alphas. Our algorithm altogether bypasses combining alphas with weights into "alpha combos". Simply put, we have developed a new method for trading alphas which does not involve combining them. This yields…

Paper proposes a new framework to mine synergistic formulaic alphas for better stock trend forecasting.

Alpha-R1 uses LLMs to reason about economic factors and news for better alpha screening.

New method estimates log-determinant using trace powers, avoiding classical limitations.

We propose a framework for constructing factor models for alpha streams. Our motivation is threefold. 1) When the number of alphas is large, the sample covariance matrix is singular. 2) Its out-of-sample stability is challenging. 3) Optimization of investment allocation into alpha streams can be tractable for a factor …

We compute the analytic expression of the probability distributions F{FTSE100,+} and F{FTSE100,-} of the normalized positive and negative FTSE100 (UK) index daily returns r(t). Furthermore, we define the alpha re-scaled FTSE100 daily index positive returns r(t)^alpha and negative returns (-r(t))^alpha that we call, aft…

In terms of the stock exchange returns, we compute the analytic expression of the probability distributions F{DAX,+} and F{DAX,-} of the normalized positive and negative DAX (Germany) index daily returns r(t). Furthermore, we define the alpha re-scaled DAX daily index positive returns r(t)^alpha and negative returns (-…

Alpha-GPT 2.0 integrates human insights into AI-driven investment research.

It is well known that combining multiple hedge fund alpha streams yields diversification benefits to the resultant portfolio. Additionally, crossing trades between different alpha streams reduces transaction costs. As the number of alpha streams increases, the relative turnover of the portfolio decreases as more trades…

RiskMiner discovers formulaic alphas using MCTS for better performance.

Internal crossing of trades between multiple alpha streams results in portfolio turnover reduction. Turnover reduction can be modeled using the correlation structure of the alpha streams. As more and more alphas are added, generally turnover reduces. In this note we use a factor model approach to address the question o…

Enhances genetic programming for stock alpha discovery with warm start and structural constraints.

We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications typically there is insufficient history to compute a sample covariance matrix (SCM) for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted) regression ove…

Unified convergence analysis of alpha-SVRG under strong convexity.

AlphaEval evaluates alpha mining models efficiently and comprehensively.

New methods for tuning alpha in Gibbs posteriors improve speed and accuracy.

An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wave vectors k and l the curvature becomes positive for alpha > alpha_0, where 0 < alpha_0 < 1 is of the order 1/k. This suggests that the flow…

The weak variance-alpha-gamma process is a multivariate Lévy process constructed by weakly subordinating Brownian motion, possibly with correlated components with an alpha-gamma subordinator. It generalises the variance-alpha-gamma process of Semeraro constructed by traditional subordination. We compare three calibrati…

We give a simple explicit formula for turnover reduction when a large number of alphas are traded on the same execution platform and trades are crossed internally. We model turnover reduction via alpha correlations. Then, for a large number of alphas, turnover reduction is related to the largest eigenvalue and the corr…

AlphaSAGE mines diverse alphas via GFlowNets, overcoming RL issues.

We give an explicit algorithm and source code for extracting equity risk factors from dead (a.k.a. "flatlined" or "hockey-stick") alphas and using them to improve performance characteristics of good (tradable) alphas. In a nutshell, we use dead alphas to extract directions in the space of stock returns along which ther…

PPO optimizes LLM-generated alpha weights for better trading performance.

The paper presents methods to improve uncertainty calibration in Bayesian Neural Networks.

AlphaForge mines and dynamically combines alpha factors for better investment performance.

In these notes we discuss investment allocation to multiple alpha streams traded on the same execution platform, including when trades are crossed internally resulting in turnover reduction. We discuss approaches to alpha weight optimization where one maximizes P&L subject to bounds on volatility (or Sharpe ratio). The…

Mannheim curves are defined for immersed curves in 3-dimensional sphere S^3 . The definition is given by considering the geodesics of S^3. First, two special geodesics, called principal normal geodesic and binormal geodesic, of S^3 are defined by using Frenet vectors of a curve immersed in S^3. Later, the curve alpha i…

AlphaCFG discovers alpha factors using grammar-guided search.

We present explicit formulas - that are also computer code - for 101 real-life quantitative trading alphas. Their average holding period approximately ranges 0.6-6.4 days. The average pair-wise correlation of these alphas is low, 15.9%. The returns are strongly correlated with volatility, but have no significant depend…

The paper evaluates biased methods for alpha-divergence minimization.

Given a smooth, closed, oriented 4-manifold X and alpha in H_2(X,Z) such that alpha.alpha > 0, a closed 2-form w is constructed, Poincare dual to alpha, which is symplectic on the complement of a finite set of unknotted circles. The number of circles, counted with sign, is given by d = (c_1(s)^2 -3sigma(X) -2chi(X))/4,…

Unbiased methods for alpha-divergence minimization struggle in high dimensions.

Paper proposes a new REINFORCE algorithm for mining formulaic alpha factors with reduced variance.

We present conditions under which positive alpha exists in the realm of active portfolio management- in contrast to the controversial result in Jarrow (2010, pg. 20) which implicates delegated portfolio management by surmising that positive alphas are illusionary. Specifically, we show that the critical assumption used…

In this paper, the geometric meaning of (alpha,beta)-norms is made clear. On this basis, we introduce a new class of Finsler metrics called general (alpha,beta)-metrics, which are defined by a Riemannian metric and an 1-form. These metrics not only generalize original (alpha,beta)-metrics naturally, but also include so…

Hybrid ML ensemble predicts market risk and generates alpha.

We discuss investment allocation to multiple alpha streams traded on the same execution platform with internal crossing of trades and point out differences with allocating investment when alpha streams are traded on separate execution platforms with no crossing. First, in the latter case allocation weights are non-nega…

We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen's original construction for Riemann surfaces and using zeta regularized determinant of Laplacians, one can endow the determinant line bundle with a natural Hermitian metric. By using …

In the present paper we study locally semiflat (we also call them semiintegrable) almost Grassmann structures. We establish necessary and sufficient conditions for an almost Grassmann structure to be alpha- or beta-semiintegrable. These conditions are expressed in terms of the fundamental tensors of almost Grassmann st…

The multi-factor model is a widely used model in quantitative investment. The success of a multi-factor model is largely determined by the effectiveness of the alpha factors used in the model. This paper proposes a new evolutionary algorithm called AutoAlpha to automatically generate effective formulaic alphas from mas…

A global twistor correspondence is established for neutral self-dual conformal structures with alpha-surface foliation when the structure is close to the standard structure on S^2 times S^2. We need to introduce some singularity for the alpha-surface foliation such that the leaves intersect on a fixed two sphere. In th…