arXiv research

A new tensorial metric describes geometry in 4D space.

We present several formulas for the traces of elements in complex hyperbolic triangle groups generated by complex reflections. The space of such groups of fixed signature is of real dimension one. We parameterise this space by a real invariant alpha of triangles in the complex hyperbolic plane. The main result of the p…

We give a purely algebro-geometric proof that if the alpha-invariant of a Q-Fano variety X is greater than dim X/(dim X+1), then (X,O(-K_X)) is K-stable. The key of our proof is a relation among the Seshadri constants, the alpha-invariant and K-stability. It also gives applications concerning the automorphism group.

It is a folk conjecture that for alpha > 1/2 there is no alpha-Hoelder surface in the subRiemannian Heisenberg group. Namely, it is expected that there is no embedding from an open subset of R^2 into the Heisenberg group that is Hoelder continuous of order strictly greater than 1/2. The Heisenberg group here is equippe…

The paper studies dynamical systems with evolving geometric structure using numerical methods.

We show that any $n$-dimensional Fano manifold $X$ with $α(X)=n/(n+1)$ and $n\geq 2$ is K-stable, where $α(X)$ is the alpha invariant of $X$ introduced by Tian. In particular, any such $X$ admits Kähler-Einstein metrics and the holomorphic automorphism group of $X$ is finite.

Alpha2 discovers logical formulaic alphas using deep reinforcement learning.

This paper summarizes closed-form relations for SE(3) maps and their derivatives.

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.

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 …

The usual construction of link invariants from quantum groups applied to the superalgebra D_{2 1,alpha} is shown to be trivial. One can modify this construction to get a two variable invariant. Unusually, this invariant is additive with respect to connected sum or disjoint union. This invariant contains an infinity of …

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…

Characterizes connections on normal distributions manifold.

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…

Researchers calculate alpha invariant for certain complex projective spaces.

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.

We compute the log canonical thresholds of non-negatively curved singular hermitian metrics on ample linearized line bundles on bi-equivariant group compactifications of complex reductive groups. To this end, we associate to any such metric a convex function whose asymptotic behavior determines the log canonical thresh…

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

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

AutoAlpha efficiently discovers effective alpha factors for quantitative investment.

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…

Let Gamma be a non-elementary Kleinian group acting on the closed n-dimensional unit ball and assume that its Poincare series converges at the exponent alpha. Let M_Gamma be the Gamma-quotient of the open unit ball. We consider certain families E = {E_1,...,E_p} of open subsets of M_Gamma such that M_Gamma minus the un…

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…

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…