arXiv research

Non-affine aggregation rules cannot preserve monotonicity in convex learning.

The reflection length of an element of a Coxeter group is the minimal number of conjugates of the standard generators whose product is equal to that element. In this paper we prove the conjecture of McCammond and Petersen that reflection length is unbounded in any non-affine Coxeter group. Among the tools used, the con…

No policy can simultaneously be fully autonomous, optimally calibrated, and helpful, proving a trilemma.

This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics $dV_{t}=κ_{t}\left(θ_{t}-V_{t}\right)dt+λ_{t}V_{t}dB_{t}$. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, e…

Embeddings are one of the fundamental building blocks for data analysis tasks. Embeddings are already essential tools for large language models and image analysis, and their use is being extended to many other research domains. The generation of these distributed representations is often a data- and computation-expensi…

We investigate specific examples of locally-defined real vector-fields on strata of translation surfaces. Integrating SL(2,R)-loci of Veech surfaces along these vector-fields yield interesting new examples of horocyle-invariant ergodic measures. These measures are supported on closed immersed manifolds with boundary th…

The paper is devoted to the investigation of four-dimensional Kahler manifolds admitting non-affine H-projective mappings. We find all such manifolds which are non-Einstein. In the paper also Kahler manifolds admitting infinitesimal H-projective transformations are determined. It is proved that the class of Kahler mani…

We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circ…

Researchers compute c-projective symmetry algebras for Kähler surfaces.

An $\varepsilon$-coreset for Least-Mean-Squares (LMS) of a matrix $A\in{\mathbb{R}}^{n\times d}$ is a small weighted subset of its rows that approximates the sum of squared distances from its rows to every affine $k$-dimensional subspace of ${\mathbb{R}}^d$, up to a factor of $1\pm\varepsilon$. Such coresets are useful…

The paper classifies knots in real projective 3-space and introduces new geometric tools.

Developed a simulation method for 3/2 stochastic volatility model.

In a financial market model, we consider the variance-optimal semi-static hedging of a given contingent claim, a generalization of the classic variance-optimal hedging. To obtain a tractable formula for the expected squared hedging error and the optimal hedging strategy, we use a Fourier approach in a general multidime…

Long term optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal strategy converge to their long-run counterparts as the investment horizon approache…

Deep nonlinear models pose a challenge for fitting parameters due to lack of knowledge of the hidden layer and the potentially non-affine relation of the initial and observed layers. In the present work we investigate the use of information theoretic measures such as mutual information and Kullback-Leibler (KL) diverge…

New samplers improve MCMC efficiency in high dimensions.

New framework discovers non-affine continuous symmetries in neural networks.

AugurOne trains single image generators without GANs using image warps.

In this paper we propose a new model for pricing stock and dividend derivatives. We jointly specify dynamics for the stock price and the dividend rate such that the stock price is positive and the dividend rate non-negative. In its simplest form, the model features a dividend rate that is mean-reverting around a consta…

This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR)…

Let F be R or C, d the dimension of F over R. Denote by P(F) either the affine plane A(F) or the hyperbolic plane H(F) over F. An arrangement L of k lines in P(F) (pairwise non-parallel in the hyperbolic case) has a link at infinity K(L) comprising k unknotted (d-1)-spheres in the (2d-1)-sphere, whose topology reflects…

We investigate the joint description of the interest-rate term stuctures of Italy and an AAA-rated European country by mean of a --here proposed-- correlated CIR-like bivariate model where one of the state variables is interpreted as a benchmark risk-free rate and the other as a credit spread. The model is constructed …

Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.

This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented by an Itô's diffusion with time--dependent drift, and with a full matrix of corre…

In [13], it is proved that any subgroup of $\mathrm{Diff}_{+}^{ω}(I)$ (the group of orientation preserving analytic diffeomorphisms of the interval) is either metaabelian or does not satisfy a law. A stronger question is asked whether or not the Girth Alternative holds for subgroups of $\mathrm{Diff}_{+}^{ω}(I)$. In th…

Study boundary actions on CAT(0) spaces, proving topological freeness.

Randomizes AD models for better option pricing.

Mixed RL improves RL efficiency with dual representations.

Sharp inequality for eigenvalues of convex bodies, proving ellipsoid uniqueness.

Supervised deep learning methods for segmentation require large amounts of labelled training data, without which they are prone to overfitting, not generalizing well to unseen images. In practice, obtaining a large number of annotations from clinical experts is expensive and time-consuming. One way to address scarcity …

New algorithm reduces regret in bandit optimization for high-dimensional data.

The paper is devoted to the local classification of generic control-affine systems on an n-dimensional manifold with scalar input for any n>3 or with two inputs for n=4 and n=5, up to state-feedback transformations, preserving the affine structure. First using the Poincare series of moduli numbers we introduce the intr…

Theory models nonlinear soft tissue elasticity and remodeling using extended Finsler geometry.

This paper explores gradient flows for sampling distributions without normalization constants.