Related papers: Calibration of Chaotic Models for Interest Rates
The oscillations of the human heart rate are inherently complex and non-linear -- they are best described by mathematical chaos, and they present a challenge when applied to the practical domain of cardiovascular health monitoring in…
In this study, we precisely evaluated the feasibility of the chaotic inflation model within a non-canonical kinetic framework. By applying the slow-roll approximation and imposing constraints on the equilateral non-Gaussianity $f_{\rm…
Addressing the uncertainty introduced by increasing renewable integration is crucial for secure power system operation, yet capturing it while preserving the full nonlinear physics of the grid remains a significant challenge. This paper…
The chaotic phase of the tilted Bose-Hubbard model is identified as a function of energy, tilt strength and particle interaction, from the eigenstate structure and the statistical features of the energy spectrum. Our analysis reveals that…
A numerically efficient inverse method for parametric model uncertainty identification using maximum likelihood estimation is presented. The goal is to identify a probability model for a fixed number of model parameters based on a set of…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
The study efforts to explore and extend the crisis predictability by synthetically reviewing and comparing a full mixture of early warning models into two constitutions: crisis identifications and predictive models. Given empirical results…
We tackle the calibration of the so-called Stochastic-Local Volatility (SLV) model. This is the class of financial models that combines the local and stochastic volatility features and has been subject of the attention by many researchers…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Model error estimation remains one of the key challenges in uncertainty quantification and predictive science. For computational models of complex physical systems, model error, also known as structural error or model inadequacy, is often…
Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but…
In agreement with the recent research findings in the econophysics, we propose that the nonlinear dynamic chaos can be generated by the turbulent capital flows in both the quantitative easing transmission channels and the transaction…
We propose the Kolmogorov stochasticity parameter, $\lambda$ for energy level spectra to classify quantum systems with corresponding classical dynamics ranging from integrable to chaotic. We also study the probability distribution function…
Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computational approach to solve stochastic partial differential…
When interest rate dynamics are described by the Libor Market Model as in BGM97, we show how some essential risk-management results can be obtained from the dual of the calibration program. In particular, if the objetive is to maximize…
As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly…
The problem of statistical inference for open chaotic systems measured with error is complicated by the interaction of the uncertainty introduced by chaos, and the various sources of random or external variation. Here a method of…
Perturbation-based explanations are widely utilized to enhance the transparency of modern machine-learning models. However, their reliability is often compromised by the unknown model behavior under the specific perturbations used. This…
To make research of chaos more friendly with discrete equations, we introduce the concept of an unpredictable sequence as a specific unpredictable function on the set of integers. It is convenient to be verified as a solution of a discrete…
Long maturity options or a wide class of hybrid products are evaluated using a local volatility type modelling for the asset price S(t) with a stochastic interest rate r(t). The calibration of the local volatility function is usually…