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.
Extracts interpretable potential energy from Hamiltonian systems.
The problem of gauging a closed form is considered. When the target manifold is a simple Lie group G, it is seen that there is no obstruction to the gauging of a subgroup H\subset G if we may construct from the form a cocycle for the relative Lie algebra cohomology (or for the equivariant cohomology), and an explicit g…
Survey on closed-form Fisher-Rao distance expressions.
The paper introduces closed-form expressions for interpreting Tsetlin Machines.
This paper provides a dictionary of closed-form kernel mean embeddings.
The paper derives closed-form approximations for mean-reverting SABR models and calibrates them to equity volatilities.
We compare two statistical models of three binary random variables. One is a mixture model and the other is a product of mixtures model called a restricted Boltzmann machine. Although the two models we study look different from their parametrizations, we show that they represent the same set of distributions on the int…
Improved portfolio optimization using VaR and CVaR with NMVM models.
New model captures complex relationships from experimental data.
Naz and Chaudhry [3] established multiple closed-form solutions for the basic Lucas-Uzawa model. According to Boucekkine and Ruiz-Tamarit [1] and Chilarescu [2] unique closed-form solutions exist for the basic Lucas-Uzawa model. We equate expressions for variables h(t) and u(t). We provide here condition for the unique…
DCFSC uses a simple auto-encoder for subspace clustering without parameters.
FDR criterion simplifies complex causal graphs to a standard front-door setting.
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differ…
Proof shows Chern form is closed on groupoid convolution algebra.
The paper uses moment matching method for pricing spread options under Lévy models.
We define and calculate the HOMFLY polynomial for a specific type of quiver.
Develops a TQFT framework to compute invariants of three-manifolds.
We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation leads to a unified (works for arbitrary dimension) method of computing the modula…
In this paper, we detail the main simulation methods used in practice to measure one-year reserve risk, and describe the bootstrap method providing an empirical distribution of the Claims Development Result (CDR) whose variance is identical to the closed-form expression of the prediction error proposed by Wüthrich et a…
The paper derives risk measures for metalog distributions.
Yau proved an existence theorem for Ricci-flat Kähler metrics in the 1970's, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions…
We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special holonomy. For forms of degree four, multi-moment maps are guaranteed to exist and a…
We solve the ANOVA decomposition for categorical inputs.
This contribution summarizes the results on the asymptotic performance of several variants of the FastICA algorithm. A number of new closed-form expressions are presented.
MDMA provides closed-form marginals and conditionals for deep networks.
Researchers develop Malliavin calculus for signatures, simplifying option Greeks computation.
This work studies Gaussian geometry under entropy-regularized 2-Wasserstein distance.
We introduce scalable deep kernels, which combine the structural properties of deep learning architectures with the non-parametric flexibility of kernel methods. Specifically, we transform the inputs of a spectral mixture base kernel with a deep architecture, using local kernel interpolation, inducing points, and struc…
We find the maximum mutual information for neural networks and its key determinants.
Unified framework for pricing various debt securities.
Bayesian neural networks learn weights with closed-form updates.
Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper proposes a new generative model, a dynamic version of the log-linear topic model o…
Motivated by the HRRT-formula for holographic entanglement entropy, we consider the following question: what are the position and the surface area of extremal surfaces in a perturbed geometry, given their anchor on the asymptotic boundary? We derive explicit expressions for the change in position and surface area, ther…
We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a Lie algebra of symmetries has invariant solutions with respect to this Lie alge…
Using Malliavin Calculus techniques, we derive closed-form expressions for the at-the-money behaviour of the forward implied volatility, its skew and its curvature, in general Markovian stochastic volatility models with continuous paths.
Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.
The paper examines optimal insurance design using Lambda-Value-at-Risk.
Universal learning machine is a theory trying to study machine learning from mathematical point of view. The outside world is reflected inside an universal learning machine according to pattern of incoming data. This is subjective pattern of learning machine. In [2,4], we discussed subjective spatial pattern, and estab…
The paper connects knot homology, quantum 6j-symbols, and complements of knots.
We establish a correspondence between Young diagrams and differential operators of infinitely many variables. These operators form a commutative associative algebra isomorphic to the algebra of the conjugated classes of finite permutations of the set of natural numbers. The Schur functions form a complete system of com…
In this paper we study a class of insurance products where the policy holder has the option to insure of its annual Operational Risk losses in a horizon of years. This involves a choice of out of years in which to apply the insurance policy coverage by making claims against losses in the given year. The…
This note finds closed-form solutions for mean-risk portfolios using a specific type of mixture distribution.
Unified method for deriving ridgelet transforms for various neural network architectures.
Study the expressivity and training complexity of polynomial neural networks.
New method calculates DMN log-likelihood faster.
The paper explores the pentagon relation and its algebraic forms.
We conjecture a closed-form expression of HOMFLY-PT invariants of double twist knots colored by rectangular Young diagrams where the twist is encoded in interpolation Macdonald polynomials. We also put forth a conjecture of cyclotomic expansions of HOMFLY-PT polynomials colored by rectangular Young diagrams for any kno…
Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility through properties of nonlinear hydrodynamics. Solitary waves have finite amplitude and spread with constant speed and constant shape. In this paper, we have used Lie group of transformation method to solve (3 + 1…