scholarly journals Complex Dynamics of Credit Risk Contagion with Time-Delay and Correlated Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Tingqiang Chen ◽  
Xindan Li ◽  
Jianmin He
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Probability Distribution ◽  
Credit Risk ◽  
Resistance Coefficient ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
Credit Risk Contagion ◽  
Nonlinear Resistance ◽  
White Noises

The stochastic time-delayed system of credit risk contagion driven by correlated Gaussian white noises is investigated. Novikov’s theorem, the time-delay approximation, the path-integral approach, and first-order perturbation theory are used to derive time-delayed Fokker-Planck model and the stationary probability distribution function of the dynamical system of credit risk contagion in the financial market. Using the method of numerical simulation, the Hopf bifurcation and chaotic behaviors of credit risk contagion are analyzed when time-delay and nonlinear resistance coefficient are varied and the effects of time-delay, nonlinear resistance and the intensity and the correlated degree of correlated Gaussian white noises on the stationary probability distribution of credit risk contagion are investigated. It is found that, as the infectious scale of credit risk and the wavy frequency of credit risk contagion are increased, the stability of the system of credit risk contagion is reduced, the dynamical system of credit risk contagion gives rise to chaotic phenomena, and the chaotic area increases gradually with the increase in time-delay. The nonlinear resistance only influences the infectious scale and range of credit risk, which is reduced when the nonlinear resistance coefficient increases. In addition, the curve of the stationary probability distribution is monotone decreasing with the increase in parameters value of time-delay, nonlinear resistance, and the intensity and the correlated degree of correlated Gaussian white noises.

scholarly journals Dynamics Evolution of Credit Risk Contagion in the CRT Market

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tingqiang Chen ◽  
Jianmin He ◽  
Qunyao Yin
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Credit Risk ◽  
Resistance Coefficient ◽  
Chaotic Phenomena ◽  
Credit Risk Transfer ◽  
The Status ◽  
The One ◽  
Credit Risk Contagion ◽  
Nonlinear Resistance

This work introduces a nonlinear dynamics model of credit risk contagion in the credit risk transfer (CRT) market, which contains time delay, the contagion rate of credit risk, and nonlinear resistance. The model depicts the dynamics behavior characteristics of evolution of credit risk contagion through numerical simulation. Meanwhile, numerical simulations show that, in the CRT market, the contagion rate of credit risk and the nonlinear resistance among CRT activities participants have some significant effects on the dynamics behaviors of evolution of credit risk contagion. Specifically, on the one hand, we find that the status curve of credit risk contagion that causes some significant changes with the increase in the contagion rate of credit risk, moreover, emerges a series of Hopf bifurcation and chaotic phenomena in the process of credit risk contagion. On the other hand, Hopf bifurcation and chaotic phenomena appear in advance with the increase in the nonlinear resistance coefficient and time-delay. In addition, there are a series of periodic windows in the chaotic interval inside, including Hopf bifurcation, inverse bifurcation, and chaos.

BIFURCATION AND CHAOTIC BEHAVIOR OF CREDIT RISK CONTAGION BASED ON FITZHUGH–NAGUMO SYSTEM

2013 ◽  
Vol 23 (07) ◽  
pp. 1350117 ◽  
Author(s):  
TINGQIANG CHEN ◽  
JIANMIN HE ◽  
JINING WANG
Keyword(s):  
Time Delay ◽  
Credit Risk ◽  
White Noise ◽  
Chaotic Behavior ◽  
Gaussian White Noise ◽  
Chaotic Oscillation ◽  
System Stability ◽  
Periodic Signal ◽  
Credit Risk Contagion ◽  
Nonlinear Resistance

This work introduces a FitzHugh–Nagumo (FHN) model of credit risk contagion based on the FHN system, which contains time-delay, Gaussian white noise, delayed feedback, weak periodic signal, and nonlinear resistance. The model depicts the dynamics behavior characteristics of evolution of credit risk contagion through simulation experiments. Meanwhile, numerical simulations show that, in a financial market, the dynamics system stability of credit risk contagion is positively related to the nonlinear resistance among participants of credit activities and to the inherent recovery capability attributed to the after-credit risk impact on economic subjects. However, the dynamics system stability of credit risk contagion is negatively related to the time-delay of credit risk contagion, the strength of Gaussian white noise, and the weak-signal cycle. Furthermore, the dynamics system of credit risk contagion introduces a series of Hopf bifurcation, inverse bifurcation and different degrees of chaotic oscillation phenomena with changes in these parameters.

Exact Stationary Response Solution for Second Order Nonlinear Systems Under Parametric and External White Noise Excitations: Part II

1988 ◽  
Vol 55 (3) ◽  
pp. 702-705 ◽  
Author(s):  
Y. K. Lin ◽  
Guoqiang Cai
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Probability Distribution ◽  
White Noise ◽  
Probability Density ◽  
Detailed Balance ◽  
Stationary Probability ◽  
Probability Flow ◽  
Parametric And External Excitations ◽  
White Noises

A systematic procedure is developed to obtain the stationary probability density for the response of a nonlinear system under parametric and external excitations of Gaussian white noises. The procedure is devised by separating the circulatory portion of the probability flow from the noncirculatory flow, thus obtaining two sets of equations that must be satisfied by the probability potential. It is shown that these equations are identical to two of the conditions established previously under the assumption of detailed balance; therefore, one remaining condition for detailed balance is superfluous. Three examples are given for illustration, one of which is capable of exhibiting limit cycle and bifurcation behaviors, while another is selected to show that two different systems under two differents sets of excitations may result in the same probability distribution for their responses.

The censored Markov chain and the best augmentation

1996 ◽  
Vol 33 (03) ◽  
pp. 623-629 ◽  
Author(s):  
Y. Quennel Zhao ◽  
Danielle Liu
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
The Best Approximation ◽  
Finite Matrix ◽  
Countable State ◽  
Stationary Probabilities

Computationally, when we solve for the stationary probabilities for a countable-state Markov chain, the transition probability matrix of the Markov chain has to be truncated, in some way, into a finite matrix. Different augmentation methods might be valid such that the stationary probability distribution for the truncated Markov chain approaches that for the countable Markov chain as the truncation size gets large. In this paper, we prove that the censored (watched) Markov chain provides the best approximation in the sense that, for a given truncation size, the sum of errors is the minimum and show, by examples, that the method of augmenting the last column only is not always the best.

STATISTICAL PROPERTIES OF INTENSITY FLUCTUATION OF SATURATION LASER MODEL DRIVEN BY CROSS-CORRELATED ADDITIVE AND MULTIPLICATIVE NOISES

2010 ◽  
Vol 24 (14) ◽  
pp. 2175-2188 ◽  
Author(s):  
PING ZHU ◽  
YI JIE ZHU
Keyword(s):  
Probability Distribution ◽  
Cross Correlation ◽  
Laser Intensity ◽  
Laser System ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
Model Driven ◽  
Multiplicative Noises ◽  
Laser Model ◽  
The Stability

Statistical properties of the intensity fluctuation of a saturation laser model driven by cross-correlation additive and multiplicative noises are investigated. Using the Novikov theorem and the projection operator method, we obtain the analytic expressions of the stationary probability distribution Pst(I), the relaxation time Tc, and the normalized variance λ2(0) of the system. By numerical computation, we discussed the effects of the cross-correlation strength λ, the cross-correlation time τ, the quantum noise intensity D, and the pump noise intensity Q for the fluctuation of the laser intensity. Above the threshold, λ weakens the stationary probability distribution, speeds up the startup velocity of the laser system from start status to steady work, and attenuates the stability of laser intensity output; however, τ strengthens the stationary probability distribution and strengths the stability of laser intensity output; when λ < 0, τ speeds up the startup; on the contrast, when λ > 0, τ slows down the startup. D and Q make the relaxation time exhibit extremum structure, that is, the startup time possesses the least values. At the threshold, τ cannot generate the effects for the saturation laser system, λ expedites the startup velocity and weakens the stability of laser intensity output. Below threshold, the effects of λ and τ not only relate to λ and τ, but also relate to other parameters of the system.

scholarly journals Statistical Mechanics of Unconfined Systems: Challenges and Lessons

2021 ◽  
Vol 3 (1) ◽  
pp. 8
Author(s):  
Bruno Arderucio Costa ◽  
Pedro Pessoa
Keyword(s):  
Probability Distribution ◽  
Statistical Mechanics ◽  
Maximum Entropy ◽  
A Priori ◽  
Ideal Gas ◽  
Stationary Probability ◽  
De Sitter ◽  
Stationary Probability Distribution ◽  
Local Measurements ◽  
Priori Information

Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space of an unconfined ideal gas in an anti-de Sitter background. Notwithstanding the gas’ freedom to move in an infinite volume, we establish necessary conditions for the stationary probability distribution solving a general maximum entropy problem to be normalizable and obtain the resulting probability for a particular choice of constraints. As a part of our analysis, we develop a novel method for identifying dynamical constraints based on local measurements. With no appeal to a priori information about globally defined conserved quantities, it is therefore applicable to a much wider range of problems.

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