Phase field simulation on mechanically induced 180 degree switching in nanomagnets

The mechanically induced 180° switching of the magnetization in cylindrical nanomagnets is demonstrated through the switching dynamics simulation by a constraint-free phase field model which is fully magneto-mechanical coupled. By using the overrun behavior of the magnetization during the mechanically induced precessional switching, a deterministic 180° switching can be achieved. It is found that the residual torque resulting from the azimuthal-angle dependence of the magneto-elastic coupling and the overrun and precessional dynamics are responsible for the switching mechanism. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于货币市场结构转换利率期限结构的实证研究

基本的利率期限结构模型均未能将结构转换效应考虑进来,因此为了探讨结构转换架构下利率期限结构模型的特性,本文在中国货币市场利率数据的基础上对基本利率期限结构模型和结构转换利率期限结构模型进行了比较研究,结果发现中国货币市场利率动态中存在明显的结构转换效应,且在结构转换效应中其本身也存在着不稳定性,这充分反映了中国货币市场在发展过程中的不成熟特征.     

Measuring the coupled risks: A copula-based CVaR model

Integrated risk management for financial institutions requires an approach for aggregating risk types (such as market and credit) whose distributional shapes vary considerably. The financial institutions often ignore risks’ coupling influence so as to underestimate the financial risks. We constructed a copula-based Conditional Value-at-Risk (CVaR) model for market and credit risks. This technique allows us to incorporate realistic marginal distributions that capture essential empirical features of these risks, such as skewness and fat-tails while allowing for a rich dependence structure. Finally, the numerical simulation method is used to implement the model. Our results indicate that the coupled risks for the listed company’s stock maybe are undervalued if credit risk is ignored, especially for the listed company with bad credit quality.     

Modeling the time-changing dependence in stock markets

The time-changing dependence in stock markets is investigated by assuming the multifractional process with random exponent (MPRE) as model for actual log price dynamics. By modeling its functional parameter S(t, ω) via the square root process (S.R.) a twofold aim is obtained. From one hand both the main financial and statistical properties shown by the estimated S(t) are captured by surrogates, on the other hand this capability reveals able to model the time-changing dependence shown by stocks or indexes. In particular, a new dynamical approach to interpreter market mechanisms is given. Empirical evidences are offered by analysing the behaviour of the daily closing prices of a very known index, the Industrial Average Dow Jones (DJIA), beginning on March,1990 and ending on February, 2005.     

Bayesian semiparametric Markov switching stochastic volatility model

This paper proposes a novel Bayesian semiparametric stochastic volatility model with Markov switching regimes for modeling the dynamics of the financial returns. The distribution of the error term of the returns is modeled as an infinite mixture of Normals; meanwhile, the intercept of the volatility equation is allowed to switch between two regimes. The proposed model is estimated using a novel sequential Monte Carlo method called particle learning that is especially well suited for state‐space models. The model is tested on simulated data and, using real financial times series, compared to a model without the Markov switching regimes. The results show that including a Markov switching specification provides higher predictive power for the entire distribution, as well as in the tails of the distribution. Finally, the estimate of the persistence parameter decreases significantly, a finding consistent with previous empirical studies.     

Properties of solutions of stochastic differential equations with continuous-state-dependent switching

This work is concerned with several properties of solutions of stochastic differential equations arising from hybrid switching diffusions. The word “hybrid” highlights the coexistence of continuous dynamics and discrete events. The underlying process has two components. One component describes the continuous dynamics, whereas the other is a switching process representing discrete events. One of the main features is the switching component depending on the continuous dynamics. In this paper, weak continuity is proved first. Then continuous and smooth dependence on initial data are demonstrated. In addition, it is shown that certain functions of the solutions verify a system of Kolmogorov's backward differential equations. Moreover, rates of convergence of numerical approximation algorithms are dealt with.     

Conditionally heteroscedastic factorial HMMs for time series in finance

In this article, we develop a new approach within the framework of asset pricing models that incorporates two key features of the latent volatility: co‐movement among conditionally heteroscedastic financial returns and switching between different unobservable regimes. By combining latent factor models with hidden Markov chain models we derive a dynamical local model for segmentation and prediction of multivariate conditionally heteroscedastic financial time series. We concentrate more precisely on situations where the factor variances are modelled by univariate generalized quadratic autoregressive conditionally heteroscedastic processes. The expectation maximization algorithm that we have developed for the maximum likelihood estimation is based on a quasi‐optimal switching Kalman filter approach combined with a generalized pseudo‐Bayesian approximation, which yield inferences about the unobservable path of the common factors, their variances and the latent variable of the state process. Extensive Monte Carlo simulations and preliminary experiments obtained with daily foreign exchange rate returns of eight currencies show promising results. Copyright © 2007 John Wiley & Sons, Ltd.     

A copula-based model of speculative price dynamics in discrete time

This paper suggests a new technique to construct first order Markov processes using products of copula functions, in the spirit of Darsow et al. (1992) [10]. The approach requires the definition of (i) a sequence of distribution functions of the increments of the process, and (ii) a sequence of copula functions representing dependence between each increment of the process and the corresponding level of the process before the increment. The paper shows how to use the approach to build several kinds of processes (stable, elliptical, Farlie-Gumbel-Morgenstern, Archimedean and martingale processes), and how to extend the analysis to the multivariate setting. The technique turns out to be well suited to provide a discrete time representation of the dynamics of innovations to financial prices under the restrictions imposed by the Efficient Market Hypothesis.     

Hybrid control for tracking of invariant manifolds

This paper presents a hybrid control method that controls to unstable equilibria of nonlinear systems by taking advantage of systems’ free dynamics. The approach uses a stable manifold tracking objective in a computationally efficient, optimization-based switching control design. Resulting nonlinear controllers are closed-loop and can be computed in real-time. Our method is validated for the cart–pendulum and the pendubot inversion problems. Results show the proposed approach conserves control effort compared to tracking the desired equilibrium directly. Moreover, the method avoids parameter tuning and reduces sensitivity to initial conditions. The resulting feedback map for the cart–pendulum has a switching structure similar to existing energy based swing-up strategies. We use the Lyapunov function from these prior works to numerically verify local stability for our feedback map. However, unlike the energy based swing-up strategies, our approach does not rely on pre-derived, system-specific switching controllers. We use hybrid optimization to automate switching control synthesis on-line for nonlinear systems.     

Threshold analysis of the susceptible-infected-susceptible model on overlay networks

In this paper, we study epidemic spreading on overlay networks in which n multiple sets of links interconnect among the same nodes. By using the microscopic Markov-chain approximation (MMA) approach, we establish the conditions of epidemic outbreak for two kinds of spreading mechanisms in such an overlay network: the concatenation case and the switching case. When a uniform infection rate is set in all the subnetworks, we find the epidemic threshold for the switching case is just n times as large as that of concatenation case. We also find that the overlay network with a uniform infection rate can be considered as an equivalent (in the sense of epidemic dynamics and epidemic threshold) weighted network. To be specific, the concatenation case corresponds to the integer weighted network, while the switching case corresponds to the fractional weighted network. Interestingly, the time-varying unweighted network can be mapped into the static weighted network. Our analytic results exhibit good agreement with numerical simulations.     

Geometric partitioning and robust ad-hoc network design

We consider bounds for the price of a European-style call option under regime switching. Stochastic semidefinite programming models are developed that incorporate a lattice generated by a finite-state Markov chain regime-switching model as a representation of scenarios (uncertainty) to compute bounds. The optimal first-stage bound value is equivalent to a Value at Risk quantity, and the optimal solution can be obtained via simple sorting. The upper (lower) bounds from the stochastic model are bounded below (above) by the corresponding deterministic bounds and are always less conservative than their robust optimization (min-max) counterparts. In addition, penalty parameters in the model allow controllability in the degree to which the regime switching dynamics are incorporated into the bounds. We demonstrate the value of the stochastic solution (bound) and computational experiments using the S&P 500 index are performed that illustrate the advantages of the stochastic programming approach over the deterministic strategy.     

Distributed adaptive switching consensus control of heterogeneous multi-agent systems with switched leader dynamics

In this paper, the leader-following distributed consensus control problem is addressed for general linear multi-agent systems with heterogeneous uncertain agent dynamics and switched leader dynamics. Different from most existing results with a single linear time-invariant (LTI) leader dynamics, the leader dynamics under consideration is composed by a family of LTI models and a switching logic governing the switches among them, which is capable of generating more diverse and sophisticated reference signals to accommodate more complicated consensus control design tasks. A novel distributed adaptive switching consensus protocol is developed by incorporating the model reference adaptive control mechanism and arbitrary switching control technique, which can be synthesized by following a two-layer hierarchical design scheme. A numerical example has been used to demonstrate the effectiveness of the proposed approach.     

Modeling hybrid network dynamics under random perturbations

We define stochastic network models based on internal structural dynamics of individual nodes which undergo Markovian switching subject to noise and external shocks. Steady-state stability and reliability criteria are established in closed form and show explicit dependence on system parameters.     

A hierarchical copula-based world-wide valuation of sovereign risk

We propose a new model for the aggregation of risks that is very flexible and useful in high dimensional problems. We propose a copula-based model that is both hierarchical and hybrid (HYC for short), because: (i) the dependence structure is modeled as a hierarchical copula, (ii) it unifies the idea of the clusterized homogeneous copula-based approach (CHC for short) and its limiting version (LHC for short) proposed in Bernardi and Romagnoli (2012, 2013). Based on this, we compute the loss function of a world-wide sovereign debt portfolio which accounts for a systemic dependence of all countries, in line with a global valuation of financial risks. Our approach enables us to take into account the non-exchangeable behavior of a sovereign debts’ portfolio clustered into several classes with homogeneous risk and to recover a possible risks’ hierarchy. A comparison between the HYC loss surface and those computed through a pure limiting approach, which is commonly used in high dimensional problems, is presented and the impact of the concentration and the granularity errors is appreciated. Finally the impact of an enlargement of the dependence structure is discussed, in the contest of a geographical area sub-portfolios analysis now relevant to determine the risk contributions of subgroups under the presence of a wider dependence structure. This argument is presented in relation to the evaluation of the insurance premium and the collateral related to the designed project of an euro-insurance-bond.     

Spin-transfer torque induced reversal in magnetic domains

Using the complex stereographic variable representation for the macrospin, from a study of the nonlinear dynamics underlying the generalized Landau–Lifshitz (LL) equation with Gilbert damping, we show that the spin-transfer torque is effectively equivalent to an applied magnetic field. We study the macrospin switching on a Stoner particle due to spin-transfer torque on application of a spin-polarized current. We find that the switching due to spin-transfer torque is a more effective alternative to switching by an applied external field in the presence of damping. We demonstrate numerically that a spin-polarized current in the form of a short pulse can be effectively employed to achieve the desired macrospin switching.     

Dynamic asset allocation for varied financial markets under regime switching framework

Asset allocation among diverse financial markets is essential for investors especially under situations such as the financial crisis of 2008. Portfolio optimization is the most developed method to examine the optimal decision for asset allocation. We employ the hidden Markov model to identify regimes in varied financial markets; a regime switching model gives multiple distributions and this information can convert the static mean–variance model into an optimization problem under uncertainty, which is the case for unobservable market regimes. We construct a stochastic program to optimize portfolios under the regime switching framework and use scenario generation to mathematically formulate the optimization problem. In addition, we build a simple example for a pension fund and examine the behavior of the optimal solution over time by using a rolling-horizon simulation. We conclude that the regime information helps portfolios avoid risk during left-tail events.     

A copula entropy approach to correlation measurement at the country level

The entropy optimization approach has widely been applied in finance for a long time, notably in the areas of market simulation, risk measurement, and financial asset pricing. In this paper, we propose copula entropy models with two and three variables to measure dependence in stock markets, which extend the copula theory and are based on Jaynes’s information criterion. Both of them are usually applied under the non-Gaussian distribution assumption. Comparing with the linear correlation coefficient and the mutual information, the strengths and advantages of the copula entropy approach are revealed and confirmed. We also propose an algorithm for the copula entropy approach to obtain the numerical results. With the experimental data analysis at the country level and the economic circle theory in international economy, the validity of the proposed approach is approved; evidently, it captures the non-linear correlation, multi-dimensional correlation, and correlation comparisons without common variables. We would like to make it clear that correlation illustrates dependence, but dependence is not synonymous with correlation. Copulas can capture some special types of dependence, such as tail dependence and asymmetric dependence, which other conventional probability distributions, such as the normal p.d.f. and the Student’s t p.d.f., cannot.     

Determining the effects of observed and unobserved heterogeneity on consumer brand choice

This paper investigates the effects of heterogeneity in consumer choice behaviour. Omitted consumer heterogeneity may lead to badly biased results, and wrong inferences concerning marketing strategies to follow. In this research we study the extent and the cause of this bias. We distinguish between observed and unobserved heterogeneity, by partialing out the effects of unmeasured heterogeneity and modelling it explicitly. The following questions will be addressed: What is unobserved heterogeneity and how much of it can be explained? How should heterogeneity be incorporated in consumer choice models? A hazard model is used for the analysis. The hazard model will yield patterns of switching among brands, as well as, the effect of marketing mix variables on brand choice and purchase timing. Differences between switchers and repeat purchasers are studied and the extent to which brand choice can be explained. Our model is estimated using scanner panel data. We find that it is important to include both observed and unobserved heterogeneity in order to obtain a better fit of the model. Our results show that it may be sufficient to only include observed heterogeneity to obtain unbiased parameter estimates. Including observed heterogeneity also reduces the aggregation or heterogeneity bias in the hazard function. © 1998 John Wiley & Sons, Ltd.     

Pricing derivatives in a regime switching market with time inhomogenous volatility

This paper studies pricing derivatives in a componentwise semi-Markov (CSM) modulated market. We consider a financial market where the asset price dynamics follows a regime switching geometric Brownian motion model in which the coefficients depend on finitely many age-dependent semi-Markov processes. We further allow the volatility coefficient to depend on time explicitly. Under these market assumptions, we study locally risk minimizing pricing of a class of European options. It is shown that the price function can be obtained by solving a non-local Black–Scholes–Merton-type PDE. We establish existence and uniqueness of a classical solution to the Cauchy problem. We also find another characterization of price function via a system of Volterra integral equation of second kind. This alternative representation leads to computationally efficient methods for finding price and hedging. An explicit expression of quadratic residual risk is also obtained.     

On laws of large numbers for systems with mean-field interactions and Markovian switching

Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled by a continuous-time Markov chain. Different from the usual switching diffusions, the systems include mean-field interactions. Our effort is devoted to obtaining laws of large numbers for the underlying systems. One of the distinct features of the paper is the limit of the empirical measures is not deterministic but a random measure depending on the history of the Markovian switching process. A main difficulty is that the standard martingale approach cannot be used to characterize the limit because of the coupling due to the random switching process. In this paper, in contrast to the classical approach, the limit is characterized as the conditional distribution (given the history of the switching process) of the solution to a stochastic McKean–Vlasov differential equation with Markovian switching.