arXiv research

In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of …

Paper defines dynamical coherence for flows and proves it under specific conditions.

Study partially hyperbolic diffeomorphisms in 3D, focusing on foliations and dynamics.

Absolutely partially hyperbolic surface endomorphisms have a coherent center foliation.

In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic …

Unsupervised clustering of series using dynamic programming.

Financial markets have been extensively studied as highly complex evolving systems. In this paper, we quantify financial price fluctuations through a coupled dynamical system composed of phase oscillators. We find a Financial Coherence and Incoherence (FCI) coexistence collective behavior emerges as the system evolves …

We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space (RKHS) operators associated with dynamical systems. In particular, we show that kernel canonical correlation analysis (CCA) can be interpreted…

Anosov flow found in specific partially hyperbolic systems.

Cohesion uses deep Koopman operators to generate long-range forecasts of chaotic dynamics.

Study dynamic risk measures and performance indices using distortion functions.

We prove that dynamical coherence is an open and closed property in the space of partially hyperbolic diffeomorphisms of $\mathbb{T}^3$ isotopic to Anosov. Moreover, we prove that strong partially hyperbolic diffeomorphisms of $\mathbb{T}^3$ are either dynamically coherent or have an invariant two-dimensional torus whi…

We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data is available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze t…

We study 3-dimensional dynamically coherent partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the transverse geometry and topology of the center stable and center unstable foliations, and the dynamics within their leaves. We find a structural dichotomy for these foliations, which we u…

Develops a new method for risk diversification using dynamic risk measures.

The paper studies optimal investment using acceptability indices to maximize portfolio performance.

A tutorial on dynamic Laplacian for time-evolving data clusters.

The assessment of co-movement among metals is crucial to better understand the behaviors of the metal prices and the interactions with others that affect the changes in prices. In this study, both Wavelet Analysis and VARMA (Vector Autoregressive Moving Average) models are utilized. First, Multiple Wavelet Coherence (M…

Quantum reservoir computing needs coherence influx for effective information processing.

We examine the problem of dynamic reserving for risk in multiple currencies under a general coherent risk measure. The reserver requires to hedge risk in a time-consistent manner by trading in baskets of currencies. We show that reserving portfolios in multiple currencies $\mathbf{V}$ are time-consistent when (and only…

The correlation matrix formalism is used to study temporal aspects of the stock market evolution. This formalism allows to decompose the financial dynamics into noise as well as into some coherent repeatable intraday structures. The present study is based on the high-frequency Deutsche Aktienindex (DAX) data over the t…

We consider Lagrangian coherent structures (LCSs) as the boundaries of material subsets whose advective evolution is metastable under weak diffusion. For their detection, we first transform the Eulerian advection-diffusion equation to Lagrangian coordinates, in which it takes the form of a time-dependent diffusion or h…

Study of deep neural networks using finite-time Lyapunov exponents.

In this paper, we provide a representation theorem for dynamic capital allocation under It{ô}-L{é}vy model. We consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with generators that grow quadratic-exponentially in the control variables. Dynamic capital …

We present a deep generative model that learns disentangled static and dynamic representations of data from unordered input. Our approach exploits regularities in sequential data that exist regardless of the order in which the data is viewed. The result of our factorized graphical model is a well-organized and coherent…

Anosov diffeomorphisms with integrable subbundles have coherent dynamics and spectral rigidity.

CMC method detects causal relationships in time series data.

The paper analyzes risk measures and optimal reserve allocation strategies.

This paper deals with applications of coherent risk measures to pricing in incomplete markets. Namely, we study the No Good Deals pricing technique based on coherent risk. Two forms of this technique are presented: one defines a good deal as a trade with negative risk; the other one defines a good deal as a trade with …

We announce some results towards the classification of partially hyperbolic diffeomorphisms on 3-manifolds, and outline the proofs in the case when the diffeomorphism is dynamically coherent. Detailed proofs are long and technical and will appear later.

Several authors have recently developed risk-sensitive policy gradient methods that augment the standard expected cost minimization problem with a measure of variability in cost. These studies have focused on specific risk-measures, such as the variance or conditional value at risk (CVaR). In this work, we extend the p…

In this paper, we contribute to the literature on energy market co-movement by studying its dynamics in the time-frequency domain. The novelty of our approach lies in the application of wavelet tools to commodity market data. A major part of economic time series analysis is done in the time or frequency domain separate…

This thesis attempts to contribute to the study of differentiable dynamics both from a semi-local and global point of view. The center of study is differentiable dynamics in manifolds of dimension 3 where we are interested in the understanding of the existence and structure of attractors as well as dynamical and topolo…

Let $f:M\to M$ be a dynamically coherent partially hyperbolic diffeomorphism whose center foliation has all its leaves compact. We prove that if the unstable bundle of $f$ is one-dimensional, then the volume of center leaves must be bounded in $M$.

Dynamic risk measures follow law invariance principles over time.

Study on learning quantum dynamics without direct interaction.

BBM models short texts using biterms to improve coherence.

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strate…

We provide a dual characterisation of the weak$^*$-closure of a finite sum of cones in $L^\infty$ adapted to a discrete time filtration $\mathcal{F}_t$: the $t^{th}$ cone in the sum contains bounded random variables that are $\mathcal{F}_t$-measurable. Hence we obtain a generalisation of Delbaen's m-stability condition…

High-fidelity quantum simulations demonstrated on short-coherence hardware.

We analyze why some models resist unlearning using linear stability theory.

We show that if a partially hyperbolic diffeomorphism of a Seifert manifold induces a map in the base which has a pseudo-Anosov component then it cannot be dynamically coherent. This extends work of Bonatti, Gogolev, Hammerlindl and Potrie to the whole isotopy class. We relate the techniques with the study of certain p…

Framework for continuous-time network data representation learning.

Chimera state refers to coexistence of coherent and non-coherent phases in identically coupled dynamical units found in various complex dynamical systems. Identification of Chimera, on one hand is essential due to its applicability in various areas including neuroscience, and on other hand is challenging due to its wid…

Defines coherent manifolds and their quantum applications.

This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the second involves applying a composition of one-step coherent risk mappings. We summar…

The paper studies stability of discretized Anosov flows.

CoRe method improves time series forecasting coherency without strict constraints.