arXiv research

Closed pricing formulas for Variance Gamma model payoffs.

The paper proves $\Gamma$-convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.

New technique explains convergence in ML models with data modifications.

Study on sphere-valued maps, proving energy convergence and current limits.

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…

We consider sequences of finitely generated discrete subgroups Gamma_i=rho_i(Gamma) of a rank 1 Lie group G, where the representations rho_i are not necessarily faithful. We show that, for algebraically convergent sequences (Gamma_i), unless Gamma_i's are (eventually) elementary or contain normal finite subgroups of ar…

Paper provides GOT convergence guarantees for sub-gamma distributions and dependent samples.

Modeling stock returns and volatility using a bivariate gamma generalized Laplace law.

We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in $\mathbb{R}^3$ equipped with a director field. The energies strongly penalize the deviation of the director from the surface unit normal and control the derivatives of the director. Such type of energies for example arise…

We study the Immediate Exchange model, recently introduced by Heinsalu and Patriarca [Eur. Phys. J. B 87: 170 (2014)], who showed by simulations that the wealth distribution in this model converges to a Gamma distribution with shape parameter $2$. Here we justify this conclusion analytically, in the infinite-population…

Adversarial meta-learning computes Gamma-minimax estimators for vague prior knowledge.

Paper studies central bank's strategy to control systemic risk in interbank system.

Let F be a family of Borel measurable functions on a complete separable metric space. The gap (or fat-shattering) dimension of F is a combinatorial quantity that measures the extent to which functions f in F can separate finite sets of points at a predefined resolution gamma > 0. We establish a connection between the g…

Proves weak convergence equals mean convergence in GGC.

The edge partition model (EPM) is a fundamental Bayesian nonparametric model for extracting an overlapping structure from binary matrix. The EPM adopts a gamma process ($Γ$P) prior to automatically shrink the number of active atoms. However, we empirically found that the model shrinkage of the EPM does not typically wo…

Study proposes a nonlocal approximation of the Willmore functional using fractional Allen-Cahn energies.

Modeling volatility with Chained Gamma Distributions for financial time series.

We address the problem of regret minimization in logistic contextual bandits, where a learner decides among sequential actions or arms given their respective contexts to maximize binary rewards. Using a fast inference procedure with Polya-Gamma distributed augmentation variables, we propose an improved version of Thomp…

We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and converge to global optima despite nonconvexity. Moreover, they turn out to be mu…

The paper models and predicts co-occurrence counts using Gamma regression.

If Gamma is any finite graph, then the unlabelled configuration space of n points on Gamma, denoted UC^n(Gamma), is the space of n-element subsets of Gamma. The braid group of Gamma on n strands is the fundamental group of UC^n(Gamma). We apply a discrete version of Morse theory to these UC^n(Gamma), for any n and any …

Study on gamma-related OU processes with simulation methods.

Introduces a new spectral geometry framework with dissipative data.

We consider complex projective space P^{n} and a smooth closed curve gamma in P^{n}. Harvey and Lawson have defined the notion of the projective hull \hat{K} of a compact subset K in P^n. This concept is an analogue of the polynomial hull of compact subsets of C^{n}. In the present note we study the relation between th…

Develops Bayesian inference methods for gamma models.

Let Gamma_k be the lower central series of a surface group Gamma of a compact surface S with one boundary component. A simple question to ponder is whether a mapping class of S can be determined to be pseudo-Anosov given only the data of its action on Gamma/Gamma_k for some k. In this paper, to each mapping class f whi…

Mixture models with Gamma and or inverse-Gamma distributed mixture components are useful for medical image tissue segmentation or as post-hoc models for regression coefficients obtained from linear regression within a Generalised Linear Modeling framework (GLM), used in this case to separate stochastic (Gaussian) noise…

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either…

We consider discrete subgroups Gamma of the simply connected Lie group SU~(1,1), the universal cover of SU(1,1), of finite level, i.e. the subgroup intersects the centre of SU~(1,1) in a subgroup of finite index, this index is called the level of the group. The Killing form induces a Lorentzian metric of constant curva…

Let G=SO(n,1) and Gamma a geometrically finite Zariski dense subgroup of G which is contained in an arithmetic subgroup of G. Denoting by Gamma(q) the principal congruence subgroup of Gamma of level q, and fixing a positive number λ_0 strictly smaller than (n-1)^2/4, we show that, as q tends to infinity along primes, t…

The paper analyzes a five-parameter Variance-Gamma model for European option pricing.

We present a class of Lévy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an underlying bilateral Gamma pr…

There is an established bijection between finite-index subgroups Gamma of Gamma(2) and bipartite graphs on surfaces, or, equivalently, certain triples of permutations. We utilize this relationship to study both congruence and noncongruence subgroups in terms of the corresponding graphs. We show some elementary criteria…

New formulas derived for variance gamma model option pricing.

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 extend Gamma index theorem to non-compact spacetimes.

For i = 1,2, let Gamma_i be a lattice in a simply connected, solvable Lie group G_i, and let X_i be a connected Lie subgroup of G_i. The double cosets Gamma_igX_i provide a foliation F_i of the homogeneous space Gamma_i\G_i. Let f be a continuous map from Gamma_1\G_1 to Gamma_2\G_2 whose restriction to each leaf of F_1…

We find the explicit expression for the equilibrium wealth distribution of the Directed Random Market process, recently introduced by Martínez-Martínez and López-Ruiz, which turns out to be a Gamma distribution with shape parameter $\frac{1}{2}$. We also prove the convergence of the discrete-time process describing the…

The article prices exchange options using variance gamma-like models.

The paper tackles learning energies from time-evolving critical points.

Let Gamma be a finitely generated, amenable group. Using an idea of E Ghys, we prove that if Gamma has a nontrivial, orientation-preserving action on the real line, then Gamma has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Gamma has a faithful action on the circle, then some finite-in…

Study shows variance gamma model outperforms Black-Scholes for USD-INR currency options.

We construct a completed version C(Gamma) of the configuration space of a linkage Gamma in R^3 which takes into account the ways one link can touch another. We also describe a simplified version of C(Gamma) which is a blow-up of the space of immersions of Gamma in R^3 A number of simple detailed examples are given.

The paper uses the variance-gamma model to price options and explain excess kurtosis.

The main result of this paper is a construction of fundamental domains for certain group actions on Lorentz manifolds of constant curvature. We consider the simply connected Lie group G~, the universal cover of the group SU(1,1) of orientation-preserving isometries of the hyperbolic plane. The Killing form on the Lie g…

The study examines how gamma positivity and PL homeomorphism types affect simplicial spheres.

The group Gamma of automorphisms of the polynomial kappa(x,y,z) = x^2 + y^2 + z^2 - xyz -2 is isomorphic to PGL(2,Z) semi-direct product with (Z/2+Z/2). For t in R, Gamma-action on ktR = kappa^{-1}(t) intersect R displays rich and varied dynamics. The action of Gamma preserves a Poisson structure defining a Gamma-invar…

Given a properly embedded graph Gamma in a ball B and a punctured sphere Sigma properly embedded in B - Gamma, we examine the conditions on Gamma that are necessary to assure that Sigma is boundary parallel.