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The purpose of this paper is to probe the recursive identification of piecewise affine Hammerstein models directly by using input-output data. To explain the identification process of a parametric piecewise affine nonlinear function, the authors prove that the inverse function corresponding to the given piecewise affine nonlinear function is also an equivalent piecewise affine form. Based on this equivalent property, during the detailed identification process with respect to piecewise affine function and linear dynamical system, three recursive least squares methods are proposed to identify those unknown parameters under the probabilistic description or bounded property of noise.

First, the basic recursive least squares method is used to identify those unknown parameters under the probabilistic description of noise. Second, multi-innovation recursive least squares method is proposed to improve the efficiency lacked in basic recursive least squares method. Third, to relax the strict probabilistic description on noise, the authors provide a projection algorithm with a dead zone in the presence of bounded noise and analyze its two properties.

Based on complex mathematical derivation, the inverse function of a given piecewise affine nonlinear function is also an equivalent piecewise affine form. As the least squares method is suited under one condition that the considered noise may be a zero mean random signal, a projection algorithm with a dead zone in the presence of bounded noise can enhance the robustness in the parameter update equation.

To the best knowledge of the authors, this is the first attempt at identifying piecewise affine Hammerstein models, which combine a piecewise affine function and a linear dynamical system. In the presence of bounded noise, the modified recursive least squares methods are efficient in identifying two kinds of unknown parameters, so that the common set membership method can be replaced by the proposed methods.

The purpose of this paper is to consider a discrete‐time, Markov, regime‐switching, affine term‐structure model for valuing bonds and other interest rate securities. The proposed model incorporates the impact of structural changes in (macro)‐economic conditions on interest‐rate dynamics. The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account.

The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account.

The authors derive a simple way to give exponential affine forms of bond prices using backward induction. The authors also consider a continuous‐time extension of the model and derive exponential affine forms of bond prices using the concept of stochastic flows.

The methods and results presented in the paper are new.

Recent U.S. Treasury yields have been constrained to some extent by the zero lower bound (ZLB) on nominal interest rates. Therefore, we compare the performance of a standard affine Gaussian dynamic term structure model (DTSM), which ignores the ZLB, to a shadow-rate DTSM, which respects the ZLB. Near the ZLB, we find notable declines in the forecast accuracy of the standard model, while the shadow-rate model forecasts well. However, 10-year yield term premiums are broadly similar across the two models. Finally, in applying the shadow-rate model, we find no gain from estimating a slightly positive lower bound on U.S. yields.

We evaluate the performance of fixed income mutual funds using stochastic discount factors motivated by continuous-time term structure models. Time-aggregation of these models for discrete returns generates new empirical “factors,” and these factors contribute significant explanatory power to the models. We provide a conditional performance evaluation for US fixed income mutual funds, conditioning on a variety of discrete ex-ante characterizations of the states of the economy. During 1985–1999 we find that fixed income funds return less on average than passive benchmarks that do not pay expenses, but not in all economic states. Fixed income funds typically do poorly when short-term interest rates or industrial capacity utilization rates are high, and offer higher returns when quality-related credit spreads are high. We find more heterogeneity across fund styles than across characteristics-based fund groups. Mortgage funds underperform a GNMA index in all economic states. These excess returns are reduced, and typically become insignificant, when we adjust for risk using the models.

Interest rate risk, i.e. the risk of changes in the interest rate term structure, is of high relevance in insurers' risk management. Due to large capital investments in interest rate sensitive assets such as bonds, interest rate risk plays a considerable role for deriving the solvency capital requirement (SCR) in the context of Solvency II. This paper seeks to address these issues.

In addition to the Solvency II standard model, the author applies the model of Gatzert and Martin for introducing a partial internal model for the market risk of bond exposures. After introducing calibration methods for short rate models, the author quantifies interest rate and credit risk for corporate and government bonds and demonstrates that the type of process can have a considerable impact despite comparable underlying input data.

The results show that, in general, the SCR for interest rate risk derived from the standard model of Solvency II tends to the SCR achieved by the short rate model from Vasicek, while the application of the Cox, Ingersoll, and Ross model leads to a lower SCR. For low‐rated bonds, the internal models approximate each other and, moreover, show a considerable underestimation of credit risk in the Solvency II model.

The aim of this paper is to assess model risk with focus on bonds in the market risk module of Solvency II regarding the underlying interest rate process and input parameters.

This paper seeks to develop a reliable and computationally efficient method for estimating and predicting large‐amplitude optical flows via taking into consideration their coherence along the time dimension.

Although the differential‐based techniques for estimating optical flows have long been in wide use owing to the relative simplicity of their mathematical description, their applicability is known to be limited to the situations, when the optical flow has a relatively small norm. In order to extend such method to deal with large‐amplitude optical flows, it is proposed to model the optical flow as a composition of its time‐delayed version and a complementary optical flow. The former is used to predict the current optical flow and, subsequently, to warp forward the preceding image of the tracking sequence, while the latter accounts for the residual displacements that are estimated using Kalman filtering based on the “small norm” assumption.

The study shows that taking into consideration the temporal coherence of optical flows results in considerable improvement in the quality of their estimation in the case when the amplitude of the optical flow is relatively large and, hence, the “small norm” assumption is not applicable.

In the present work, the algorithm is formulated under the assumption that the optical flow is affine. This assumption may be restrictive in practice. Consequently, an important direction to extend this work is to consider more general classes of optical flows.

The main contribution of the present study is the use of multigrid methods and a projection scheme to relate the state equation to the apparent image motion.

This paper shows that for a large class of single and multi‐factor term structure models, including the affine class, the market price of risk is directly related to the parameters of the stochastic processes of the underlying factors of the economy. It is shown that the market price of risk is proportional to the limit of the volatility of zero coupon bond returns. This means that the market price of risk is not entirely arbitrary. Not only it must be consistent with no arbitrage conditions, also it must be consistent with the parameters of stochastic processes of the factors that describe the economy. If the market price of risk is not correctly specified, then it could lead to profit opportunities of the type discussed in Backus et al (1996). Another consequence of our result is that in empirical tests of interest rate processes, the market price of risk should not be specified exogenously since its value is a function of the parameters of the model. We extend our result to forward processes. The market price of risk is shown to be a function of the volatility of the forward rate processes.

Following Ang and Piazzesi’s (2003) study, the authors use an affine term structure model to study the relevance of macroeconomic (domestic and foreign) factors for Peru’s sovereign yield curve in the period from November 2005 to December 2015. The paper aims to discuss this issue.

Risk premia are modeled as time-varying and depend on both observable and unobservable factors; and the authors estimate a vector autoregressive model considering no-arbitrage assumptions.

The authors find evidence that macro factors help to improve the fit of the model and explain a substantial amount of variation in bond yields. However, their influence is very sensitive to the specification model. Variance decompositions show that macro factors explain a significant share of the movements at the short and middle segments of the yield curve (up to 50 percent), while unobservable factors are the main drivers for most of the movements at the long end of the yield curve (up to 80 percent). Furthermore, the authors find that international markets are relevant for the determination of the risk premium in the short term. Higher uncertainty in international markets increases bond yields, although this effect vanishes quickly. Finally, the authors find that no-arbitrage restrictions with the incorporation of macro factors improve forecasts.

To the authors’ knowledge this is the first application of this type of models using data from an emerging country such as Peru.

The purpose of this paper is to establish a cheap but accurate approximation of the forward map in electrical capacitance tomography in order to approach robust real‐time inversion in the framework of Bayesian statistics based on Markov chain Monte Carlo (MCMC) sampling.

Existing formulations and methods to reduce the order of the forward model with focus on electrical tomography are reviewed and compared. In this work, the problem of fast and robust estimation of shape and position of non‐conducting inclusions in an otherwise uniform background is considered. The boundary of the inclusion is represented implicitly using an appropriate interpolation strategy based on radial basis functions. The inverse problem is formulated as Bayesian inference, with MCMC sampling used to efficiently explore the posterior distribution. An affine approximation to the forward map built over the state space is introduced to significantly reduce the reconstruction time, while maintaining spatial accuracy. It is shown that the proposed approximation is unbiased and the variance of the introduced additional model error is even smaller than the measurement error of the tomography instrumentation. Numerical examples are presented, avoiding all inverse crimes.

Provides a consistent formulation of the affine approximation with application to imaging of binary mixtures in electrical tomography using MCMC sampling with Metropolis‐Hastings‐Green dynamics.

The proposed cheap approximation indicates that accurate real‐time inversion of capacitance data using statistical inversion is possible.

The proposed approach demonstrates that a tolerably small increase in posterior uncertainty of relevant parameters, e.g. inclusion area and contour shape, is traded for a huge reduction in computing time without introducing bias in estimates. Furthermore, the proposed framework – approximated forward map combined with statistical inversion – can be applied to all kinds of soft‐field tomography problems.

The numerical simulation of dispersed-phase evolution in injection molding process of polymer blends is of great significance in both adjusting material microstructure and improving performances of the final products. This paper aims to present a numerical strategy for the simulation of dispersed-phase evolution for immiscible polymer blends in injection molding.

First, the dispersed-phase modeling is discussed in detail. Then the Maffettone–Minale model, affine deformation model, breakup model and coalescence statistical model are chosen for the dispersed-phase evolution. A general coupled model of microscopic morphological evolution and macroscopic flow field is constructed. Besides, a stable finite element simulation strategy based on pressure-stabilizing/Petrov–Galerkin/streamline-upwind/Petrov–Galerkin method is adopted for both scales.

Finally, the simulation results are compared and evaluated with the experimental data, suggesting the reliability of the presented numerical strategy.

The coupled modeling of dispersed-phase and complex flow field during injection molding and the tracing and simulation of droplet evolution during the whole process can be achieved.