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This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group affine systems.

The evolution and operation properties of error propagation model of discrete group affine physical systems are investigated in detail. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis which provide a deeper insight and are beneficial to the control and estimation of discrete group affine systems.

The investigation on the state independency and log-linearity of invariant errors for discrete group affine systems are presented in this work, and it is pivotal for the convergence and stability of estimation and control of physical systems in engineering practice. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis.

An example application to the attitude dynamics of a rigid body together with the attitude estimation problem is used to illustrate the theoretical results.

The mathematical proof and analysis of the state independency and log-linearity property are the unique and original contributions of this work.

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.

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.

Choice under risk has a large stochastic (unpredictable) component. This chapter examines five stochastic models for binary discrete choice under risk and how they combine with “structural” theories of choice under risk. Stochastic models are substantive theoretical hypotheses that are frequently testable in and of themselves, and also identifying restrictions for hypothesis tests, estimation and prediction. Econometric comparisons suggest that for the purpose of prediction (as opposed to explanation), choices of stochastic models may be far more consequential than choices of structures such as expected utility or rank-dependent utility.

In this paper we study a class of complexity measures, induced by a new data structure for representing k-valued functions (operations), called minor decision diagram. When assigning values to some variables in a function the resulting functions are called subfunctions, and when identifying some variables the resulting functions are called minors. The sets of essential variables in subfunctions of f are called separable in f.

We examine the maximal separable subsets of variables and their conjugates, introduced in the paper, proving that each such set has at least one conjugate. The essential arity gap gap(f) of the function f is the minimal number of essential variables in f which become fictive when identifying distinct essential variables in f. We also investigate separable sets of variables in functions with non-trivial arity gap. This allows us to solve several important algebraic, computational and combinatorial problems about the finite-valued functions.

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 aims to study the issues of adaptive fuzzy control for a category of switched under-actuated systems with input nonlinearities and external disturbances.

A control scheme based on sliding mode surface with a hierarchical structure is introduced to enhance the responsiveness and robustness of the studied systems. An equivalent control and switching control rules are co-designed in a hierarchical sliding mode control (HSMC) framework to ensure that the system state reaches a given sliding surface and remains sliding on the surface, finally stabilizing at the equilibrium point. Besides, the input nonlinearities consist of non-symmetric saturation and dead-zone, which are estimated by an unknown bounded function and a known affine function.

Based on fuzzy logic systems and the hierarchical sliding mode control method, an adaptive fuzzy control method for uncertain switched under-actuated systems is put forward.

The “cause and effect” problems often existing in conventional backstepping designs can be prevented. Furthermore, the presented adaptive laws can eliminate the influence of external disturbances and approximation errors. Besides, in contrast to arbitrary switching strategies, the authors consider a switching rule with average dwell time, which resolves control problems that cannot be resolved with arbitrary switching signals and reduces conservatism.

I survey applications of Markov switching models to the asset pricing and portfolio choice literatures. In particular, I discuss the potential that Markov switching models have to fit financial time series and at the same time provide powerful tools to test hypotheses formulated in the light of financial theories, and to generate positive economic value, as measured by risk-adjusted performances, in dynamic asset allocation applications. The chapter also reviews the role of Markov switching dynamics in modern asset pricing models in which the no-arbitrage principle is used to characterize the properties of the fundamental pricing measure in the presence of regimes.

The cybernetic approach differs significantly from the conventional reductionist methods of natural and biological sciences. Norbert Wiener established the theory of cybernetics as a science of control and communication process in living beings (human and animals) and machines. Dutta Majumder in his Norbert Wiener Award winning paper extended the approach to include integrated complex human machine systems and functions with general systems theory as a unitary science laying the mathematical foundation for unifying observing systems, observed systems and the act of observing as indicated in von Foerster’s concept of second‐order cybernetics. Both from the point of view of ontology and that of epistemology the cybernetic approach now enables computer technology to incorporate artificial intelligence (AI) and expert system (ES) for knowledge based instrumentation for diagnostics and therapy planning. Presents the results of a project for development of a knowledge based framework for combining different modalities of medical image processing such as CT, MR(T₁), MR(T₂), SPECT, PET, USG etc. whichever is relevant for particular pathological investigation for diagnostics and therapeutic planning. Experiments were conducted with (a) Alzheimer’s patient data and (b) detection and grading of malignancy with oncological data for the cancer screening system.

The purpose of this paper is to propose a new algorithm for detection of chaos in oscillatory circuits. The algorithm is based on the wavelet transform.

The proposed detection is developed by using a specific measure obtained by averaging wavelet coefficients. This measure exhibits various values for chaotic and periodic states.

The proposed algorithm is applied to signals from autonomous systems such as the Chua’s oscillatory circuit, the Lorenz chaotic system and non-autonomous systems such as the Duffing oscillator. In addition, the detection is applied to sequences obtained from the logistic map. The results are compared to those obtained with a detrended fluctuation analysis and a time-frequency signal analysis based on detectors of chaotic states.

In this paper, a new algorithm is proposed for the detection of chaos from a single time series. The proposed technique is robust to the noise influence, having smaller calculation complexity with respect to the state-of-the-art techniques. It is suitable for real-time detection with delay that is about half of the window width.