arXiv research

Study finds sales forecasters overreact to extreme news.

New algorithm tames non-linear growth in stochastic optimization.

Deep tensor factorization benefits from implicit regularization with polynomial growth.

Paper tackles robust control of SDEs with ambiguity, proving value function existence and applying to investment problems.

We obtain a maximum principle, and "a priori" upper estimates for solutions of a class of non linear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumption of volume growth conditions. Various applications of the results obtained are presented.

We give dimension-free regularity conditions for a class of possibly degenerate sub-elliptic equations in the Heisenberg group exhibiting super-quadratic growth in the horizontal gradient; this solves an issue raised by Manfredi & Mingione (Math. Ann. 2007) where only dimension dependent bounds for the growth exponent …

In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver $g$ is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of $g$-Snell enveloppe. Then, in a second step, we re…

From the Hamilton-Jacobi-Bellman equation for the value function we derive a non-linear partial differential equation for the optimal portfolio strategy (the dynamic control). The equation is general in the sense that it does not depend on the terminal utility and provides additional analytical insight for some optimal…

We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction o…

In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of the…

The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems model…

We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We apply this novel methodology to five population growth models, including models …

The vanishing of reduced $\ell^2$-cohomology for amenable groups can be traced to the work of Cheeger & Gromov. The subject matter here is reduced $\ell^p$-cohomology for $p \in ]1,\infty[$, particularly its vanishing. Results showing its triviality are obtained, for example: when $p \in ]1,2]$ and $G$ is amenable; whe…

In this article we will show that the Macro-Economy and its growth can be modelled and explained exactly in principle by commonly known Field Theory from theoretical physics. We will show the main concepts and calculations needed and show that calculation and prediction of economic growth then gets indeed possible in D…

We study the existence of solutions of the non-linear differential equations on the compact Riemannian manifolds $(M^n,g), n\geq 2$, Δ_p u + a(x)u^{p-1} = λf(u,x), (E2) where $Δ_p$ is the $p-$laplacian, with $1<p<n$. The equation (E2) generalizes a equation considered by Aubin, where he has considered, a compact Rieman…

We propose a simple non-equilibrium model of a financial market as an open system with a possible exchange of money with an outside world and market frictions (trade impacts) incorporated into asset price dynamics via a feedback mechanism. Using a linear market impact model, this produces a non-linear two-parametric ex…

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after …

In this paper, we analyze a real-valued reflected backward stochastic differential equation (RBSDE) with an unbounded obstacle and an unbounded terminal condition when its generator $f$ has quadratic growth in the $z$-variable. In particular, we obtain existence, comparison, and stability results, and consider the opti…

Voluntary insurance contracts constitute a puzzle because they increase the expectation value of one party's wealth, whereas both parties must sign for such contracts to exist. Classically, the puzzle is resolved by introducing non-linear utility functions, which encode asymmetric risk preferences; or by assuming the p…

The geometric evolution equations provide new ways to address a variety of non-linear problems in Riemannian geometry, and, at the same time, they enjoy numerous physical applications, most notably within the renormalization group analysis of non-linear sigma models and in general relativity. They are divided into clas…

New method estimates SDE parameters efficiently using WCE and SGD.

JFR-rg model explains Japan's stable debt despite high interest rates and low growth.

A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman and Zhou (1993). We wor…

In recent years, there has been an exponential growth in the number of complex documents and texts that require a deeper understanding of machine learning methods to be able to accurately classify texts in many applications. Many machine learning approaches have achieved surpassing results in natural language processin…

Antifreeze proteins (AFPs) are the sub-set of ice binding proteins indispensable for the species living in extreme cold weather. These proteins bind to the ice crystals, hindering their growth into large ice lattice that could cause physical damage. There are variety of AFPs found in numerous organisms and due to the h…

Despite the phenomenal success of deep learning in recent years, there remains a gap in understanding the fundamental mechanics of neural nets. More research is focussed on handcrafting complex and larger networks, and the design decisions are often ad-hoc and based on intuition. Some recent research has aimed to demys…

Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a stochastic and non-linear extension of the classical Stefan-problem in one space dimension, where the paths of the moving in…

Stylized facts of empirical assets log-returns $Z$ include the existence of (semi) heavy tailed distributions $f_Z(z)$ and a non-linear spectrum of Hurst exponents $τ(β)$. Empirical data considered are daily prices of 10 large indices from 01/01/1990 to 12/31/2004. We propose a stylized model of price dynamics which is…

Managing data storage growth is of crucial importance to businesses. Poor practices can lead to large data and financial losses. Access to storage information along with timely action, or capacity forecasting, are essential to avoid these losses. In addition, ensuring high accuracy of capacity forecast estimates along …

National statistical systems are the enterprises tasked with collecting, validating and reporting societal attributes. These data serve many purposes - they allow governments to improve services, economic actors to traverse markets, and academics to assess social theories. National statistical systems vary in quality, …

Proposes a low-rank bilinear pooling model for link prediction in knowledge graphs.

In this paper we obtain generalized Keller-Osserman conditions for wide classes of differential inequalities on weighted Riemannian manifolds of the form $L u\geq b(x) f(u) \ell(|\nabla u|)$ and $L u\geq b(x) f(u) \ell(|\nabla u|) - g(u) h(|\nabla u|)$, where $L$ is a non-linear diffusion-type operator. Prototypical ex…

Historical economic growth in countries of the former USSR is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used, but not analysed, during the formulation of this theory. Unified Growth Theory does not explain the mechanism of economic growth. It explains the mechanism of Malt…

The Unified Growth Theory is a puzzling collection of myths based on illusions created by hyperbolic distributions. Some of these myths are discussed. The examination of data shows that the three stages of growth (Malthusian Regime, Post-Malthusian Regime and Modern Growth Regime) did not exist and that Industrial Revo…

Historical economic growth in Asia (excluding Japan) is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used (but not analysed) during the formulation of this theory. Unified Growth Theory does not explain the mechanism of economic growth. It explains the mechanism of Malthusian…

Study confined subgroups in groups with contracting elements, showing their growth rate is strictly greater than half of the ambient growth rate.

Growth rate of the world Growth Domestic Product (GDP) is analysed to determine possible pathways of the future economic growth. The analysis is based on using the latest data of the World Bank and it reveals that the growth rate between 1960 and 2014 was following a trajectory approaching asymptotically a constant val…

Historical economic growth in Latin America is analysed using the data of Maddison. Unified Growth Theory is found to be contradicted by these data in the same way as it is contradicted by the economic growth in Africa, Asia, former USSR, Western Europe, Eastern Europe and by the world economic growth. Paradoxically, U…

Growth rates of geodesics on modular orbifolds are studied.

Data describing historical economic growth are analysed. Included in the analysis is the world and regional economic growth. The analysis demonstrates that historical economic growth had a natural tendency to follow hyperbolic distributions. Parameters describing hyperbolic distributions have been determined. A search …

The study provides volume growth estimates for specific types of manifolds.

Study growth rates of subgroups in groups with a constricting element.

We present a quantitative characterisation of the fluctuations of the annualized growth rate of the real US GDP per capita growth at many scales, using a wavelet transform analysis of two data sets, quarterly data from 1947 to 2015 and annual data from 1800 to 2010. Our main finding is that the distribution of GDP grow…

Paper reviews and proves volume growth estimates for different types of gradient Ricci solitons.

Study groups with polynomial growth, finding structure and applications.

In many European countries the growth of the real GDP per capita has been linear since 1950. An explanation for this linearity is still missing. We propose that in artificial intelligence we may find models for a linear growth of performance. We also discuss possible consequences of the fact that in systems with linear…

Introduced by Gromov in the nineties, the systolic growth of a Lie group gives the smallest possible covolume of a lattice with a given systole. In a simply connected nilpotent Lie group, this function has polynomial growth, but can grow faster than the volume growth. We express this systolic growth function in terms o…

New proof shows not all Salem numbers are growth rates of Coxeter groups.