Analytic Representation of a General Multi-Factor Pricing Kernel

Matrix Green's function solution of closed-form singularity for functionally graded and transversely isotropic materials under circular ring force vector

We present a pricing kernel that summarizes well the main features of the dynamics of interest rates and risk in postwar U.S. data and use it to uncover how the pricing kernel has moved with the short rate in this data. Our findings imply that standard monetary models miss an essential link between the central bank instrument and the economic activity that monetary policy is intended to affect, and thus we call for a new approach to monetary policy analysis. We sketch a new approach using an economic model based on our pricing kernel. The model incorporates the key relationships between policy and risk movements in an unconventional way: the central bank's policy changes are viewed as primarily intended to compensate for exogenous business cycle fluctuations in risk that threaten to push inflation off target. This model, while an improvement on standard models, is considered just a starting point for their revision. It leads to critical questions that researchers need to answer as they continue to revise their approach to monetary policy analysis. Copyright © 2009 by the National Bureau of Economic Research.

Green's function solution and displacement potentials for Transformed Transversely Isotropic materials

Green's function solution of temperature field for flow in porous passages

This paper presents a new approach to interest rate dynamics. We consider the general family of arbitrage-free positive interest rate models, valid on all time horizons, in the case of a discount bond system driven by a Brownian motion of one or more dimensions. We show that the space of such models admits a canonical mapping to the space of square-integrable Wiener functionals. This is achieved by means of a conditional variance representation for the state price density. The Wiener chaos expansion technique is then used to formulate a systematic analysis of the structure and classification of interest rate models. We show that the specification of a first-chaos model is equivalent to the specification of an admissible initial yield curve. A comprehensive development of the second-chaos interest rate theory is presented in the case of a single Brownian factor, and we show that there is a natural methodology for calibrating the model to at-the-money-forward caplet prices. The factorisable second-chaos models are particularly tractable, and lead to closed-form expressions for options on bonds and for swaptions. In conclusion we outline a general “international” model for interest rates and foreign exchange, for which each currency admits an associated family of discount bonds, and show that the entire system can be generated by a vector of Wiener functionals.

By assuming that the stochastic discount factor (SDF) [Formula: see text] is a proper but unspecified function of state variables [Formula: see text], we show that this function [Formula: see text] must solve a simple second-order linear differential equation specified by state variables’ risk-neutral dynamics. Therefore, this assumption determines the most general possible SDFs and associated preferences, that are consistent with the given risk-neutral state dynamics and interest rate. A consistent SDF then implies the corresponding state dynamics in the data-generating measure. Our approach offers novel flexibilities to extend several popular asset pricing frameworks: affine and quadratic interest rate models, as well as models built on linearity-generating processes. We illustrate the approach with an international asset pricing model in which (i) interest rate has an affine dynamic term structure and (ii) the forward premium puzzle is consistent with consumption-risk rationales; the two asset pricing features previously deemed conceptually incompatible.

Several ultrasound-based techniques for the estimation of soft tissue elasticity are currently being investigated. Most of them study the medium response to dynamic excitations. Such responses are usually modeled in a purely elastic medium using a Green's function solution of the motion equation. However, elasticity by itself is not necessarily a discriminant parameter for malignancy diagnosis. Modeling viscous properties of tissues could also be of great interest for tumor characterization. We report in this paper an explicit derivation of the Green's function in a viscous and elastic medium taking into account shear, bulk, and coupling waves. From this theoretical calculation, 3D simulations of mechanical waves in viscoelastic soft tissues are presented. The relevance of the viscoelastic Green's function is validated by comparing simulations with experimental data. The experiments were conducted using the supersonic shear imaging (SSI) technique which dynamically and remotely excites tissues using acoustic radiation force. We show that transient shear waves generated with SSI are modeled very precisely by the Green's function formalism. The combined influences of out-of-plane diffraction, beam shape, and shear viscosity on the shape of transient waves are carefully studied as they represent a major issue in ultrasound-based viscoelasticity imaging techniques.

Green's function solutions of the biaxial and uniaxial anisotropic layered-medium planar-structure is formulated in terms of Maxwell's equations. Diagonalized biaxial and uniaxial permittivity tensors in the coordinate system of interest are treated. The Green's function is found in the double Fourier transformed domain for three longitudinal-to-an-axis coupled electric-magnetic field sets applied to a simple layered structure. The approach is applicable to structures having discontinuities in two orthogonal planar directions such as patch radiators or resonators. Spectral Green's function is usable in method-of-moment calculations assisted by Galerkin's method.

Analytic Swaption Pricing in the Black-Karasinski Model

Bermudan Swaptions in the LIBOR Market Model

Analytic solutions for 2-D incompressible Stokes' flow with lateral variations in viscosity have been developed with a Green's function method and matrix propagator techniques. The analytic solutions are developed based on the observation that lateral variations in viscosity only result in mode coupling between viscosity and buoyancy in the horizontal dimension and not in the vertical dimension. The Green's function solution for flows with a viscosity that varies laterally with an exponential function indicates that, if the lateral variation in viscosity is within one order of magnitude, at very long wavelengths (for example degree 2) the mode coupling between viscosity and buoyancy does not greatly influence the geoid deduced from models ignoring the lateral variations in viscosity. The relatively short-wavelength geoid (degree 4 and higher modes), however, is seriously contaminated by mode coupling. The solutions for sharp lateral variations in viscosity calculated with propagator matrix techniques show that the topography varies rapidly across the viscosity boundaries.

A rigorous analysis of surface acoustic wave tags for wireless identification (ID) systems is developed based on Green's function technique and method of moments. The SAW ID-tags can be fabricated using arbitrary finite reflector structures placed in multiple tracks and channels. From the Green's function solutions, the P matrix parameters for the reflector bits and coupling transducer are deduced. These P matrices are cascaded and interconnected using network analysis to account for the resulting quasi-2D structure. To provide more physical insights into the scattering mechanism, the cascaded network is described in terms of the more illuminating global reflection and transmission coefficients. Simulation of prototype SAW tag configuration is carried out. Response in time domain is presented to show the spurious signals due to multiple reflections.

This paper presents an accurate method to compute the bidirectional reflectance distribution function (BRDF) due to subsurface scattering inside the material of the objects. This computation requires iterating over the different lighting directions, and solving the integro-differential equation of light transport (scattering and absorption). Solving the light transport equation is expensive, and solving it independently for different directions adds even further to the expense. However most of the computations are very similar between directions. We make use of Green's function of the transport problem to have a better separation between computations that are independent of incident directions from those that are dependent. This allows us to avoid as much repetition in the computations as possible, thus gives us a faster BRDF computation method without any loss of accuracy. We validate our method against a standard light transport solver and use it to compute BRDF for a variety of materials.

An integral equation solution to the problem of transverse magnetic (TM) or transverse electric (TE) scattering by an isotropic dielectric/ferrite material cylinder in the presence of a perfectly conducting half-plane is presented. The technique is termed a method of moments (MM)/Green's function solution since the method of moments is used to determine the electric and magnetic polarization currents representing the material cylinder, while the presence of the half-plane is accounted for by including the half-plane Green's function in the kernel of the integral equations. Numerical results are presented for the echo width, material cylinder interior fields, and the surface impedance of a material slab on the surface of a half-plane.

We construct default-free interest rate models in the spirit of the well-known Markov functional models: our focus is analytic tractability of the models and generality of the approach. We work in the setting of state price densities and construct models by means of the so called propagation property. The propagation property can be found implicitly in all of the popular state price density approaches, in particular heat kernels share the propagation property (wherefrom we deduced the name of the approach). As a related matter, an interesting property of heat kernels is presented, too.