Related papers: Endogenous Crashes as Phase Transitions
We predict the emergence of extreme events in a parametrically driven nonlinear dynamical system using three Deep Learning models, namely Multi-Layer Perceptron, Convolutional Neural Network and Long Short-Term Memory. The Deep Learning…
We show that there exist dynamical phase transitions (DPTs), as defined in [Phys. Rev. Lett. 110 135704 (2013)], in the transverse-field Ising model (TFIM) away from the static quantum critical points. We study a class of special states…
We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…
The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail…
We propose a data-driven tracking model predictive control (MPC) scheme to control unknown discrete-time linear time-invariant systems. The scheme uses a purely data-driven system parametrization to predict future trajectories based on…
The ability to reliably predict critical transitions in dynamical systems is a long-standing goal of diverse scientific communities. Previous work focused on early warning signals related to local bifurcations (critical slowing down) and…
The paper discusses various practical consequences of treating economics and finance as an inherently dynamic and chaotic system. On the theoretical side this looks at the general applicability of the market-making pricing approach to…
Events such as the Financial Crisis of 2007-2008 or the COVID-19 pandemic caused significant losses to banks and insurance entities. They also demonstrated the importance of using accurate equity risk models and having a risk management…
The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for fractal Brownian processes: nondifferentiability, Brownian nature of process and a linear memory measure. We have…
Dynamic fault trees (DFTs) have emerged as an important tool for capturing the dynamic behavior of system failure. These DFTs are then analyzed qualitatively and quantitatively using stochastic or algebraic methods to judge the failure…
Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socio-economic changes and climate transitions between ice-ages and warm-ages. From bifurcation…
In this paper, we study the optimal capital structure model with endogenous bankruptcy when the firm's asset value follows an exponential L\'evy process with positive jumps. In the Leland-Toft framework \cite{LelandToft96}, we obtain the…
Dynamical phase transitions (DPTs), characterized by non-analytic behaviors in time domain, extend the equilibrium phase transitions to far-from-equilibrium situations. It has been predicted that DPTs can be precisely identified by the…
An extreme event is a sudden and violent change in the state of a nonlinear system. In fluid dynamics, extreme events can have adverse effects on the system's optimal design and operability, which calls for accurate methods for their…
Mathematical programming formulations of influence diagrams can bridge the gap between representing and solving decision problems. However, they suffer from both modeling and computational limitations. Aiming to address modeling…
Stock price prediction is vital for investment decisions and risk management, yet remains challenging due to markets' nonlinear dynamics and time-varying inter-stock correlations. Traditional static-correlation models fail to capture…
We consider the dynamics of a 1D system evolving according to a deterministic drift and randomly forced by two types of jumps processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously…
The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…
This work proposes an innovative approach using machine learning to predict extreme events in time series of chaotic dynamical systems. The research focuses on the time series of the H\'enon map, a two-dimensional model known for its…
A taxonomy of large financial crashes proposed in the literature locates the burst of speculative bubbles due to endogenous causes in the framework of extreme stock market crashes, defined as falls of market prices that are outlier with…