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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.

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.

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.

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.

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 purpose of this paper is to derive semi‐closed‐form solutions to a wide variety of interest rate derivatives prices under stochastic volatility in affine‐term structure models.

The paper first derives the Frobenius series solution to the cross‐moment generating function, and then inverts the related characteristic function using the Gauss‐Laguerre quadrature rule for the corresponding cumulative probabilities.

This paper values options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars, etc. The valuation approach suggested in this paper is found to be both accurate and fast and the approach compares favorably with some alternative methods in the literature.

Future research could extend the approach adopted in this paper to some non‐affine‐term structure models such as quadratic models.

The valuation approach in this study can be used to price mortgage‐backed securities, asset‐backed securities and credit default swaps. The approach can also be used to value derivatives on other assets such as commodities. Finally, the approach in this paper is useful for the risk management of fixed‐income portfolios.

This paper utilizes a new approach to value many of the most commonly traded interest rate derivatives in a stochastic volatility framework.

The Reduced Basis Method (RBM) generates low-order models of parametrized PDEs to allow for efficient evaluation of parametrized models in many-query and real-time contexts. The purpose of this paper is to investigate the performance of the RBM in microwave semiconductor devices, governed by Maxwell's equations.

The paper shows the theoretical framework in which the RBM is applied to Maxwell's equations and present numerical results for model reduction under geometry variation.

The RBM reduces model order by a factor of $1,000 and more with guaranteed error bounds.

Exponential convergence speed can be observed by numerical experiments, which makes the RBM a suitable method for parametric model reduction (PMOR).

This paper aims to investigate an adaptive prescribed performance control problem for switched pure-feedback non-linear systems with input quantization.

By using the semi-bounded continuous condition of non-affine functions, the controllability of the system can be guaranteed. Then, a constraint variable method is introduced to ensure that the tracking error satisfies the prescribed performance requirements. Meanwhile, to avoid the design difficulties caused by the input quantization, a non-linear decomposition method is adopted. Finally, the feasibility of the proposed control scheme is verified by a numerical simulation example.

Based on neural networks and prescribed performance control method, an adaptive neural control strategy for switched pure-feedback non-linear systems is proposed.

The complex deduction and non-differentiable problems of traditional prescribed performance control methods can be solved by using the proposed error transformation approach. Besides, to obtain more general results, the restrictive differentiability assumption on non-affine functions is removed.

The purpose of this paper is to compare competing adaptive strategies for fast frequency sweeps for driven and waveguide‐mode problems and give recommendations for practical implementations.

The paper first summarizes the theory of adaptive strategies for multi‐point (MP) sweeps and then evaluates the efficiency of such methods by means of numerical examples.

The authors' numerical tests give clear evidence for exponential convergence. In the driven case, highly resonant structures lead to pronounced pre‐asymptotic regions, followed by almost immediate convergence. Bisection and greedy point‐placement methods behave similarly. Incremental indicators are trivial to implement and perform similarly well as residual‐based methods.

While the underlying reduction methods can be extended to any kind of affine parameter‐dependence, the numerical tests of this paper are for polynomial parameter‐dependence only.

The present paper describes self‐adaptive point‐placement methods and termination criteria to make MP frequency sweeps more efficient and fully automatic.

The paper provides a self‐adaptive strategy that is efficient and easy to implement. Moreover, it demonstrates that exponential convergence rates can be reached in practice.