Abstract: We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer’s assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of the firm are a geometric Brownian motion until informed equityholders optimally liquidate, we derive the conditional distribution of the assets, given accounting data and survivorship. Contrary to the perfect-information case, there exists a default-arrival intensity process. That intensity is calculated in terms of the conditional distribution of assets. Credit yield spreads are characterized in terms of accounting information. Generalizations are provided. 1 We are exceptionally grateful to Michael Harrison for his significant contributions to this paper, which are noted within. We are also grateful for insightful research assistance

There are several generalizations of the classical theory of Sobolev spaces as they are necessary for the applications to Carnot-Carathéodory spaces, subelliptic equations, quasiconformal mappings on Carnot groups and more general Loewner spaces, analysis on topological manifolds, potential theory on infinite graphs, analysis on fractals and the theory of Dirichlet forms. The aim of this paper is to present a unified approach to the theory of Sobolev spaces that covers applications to many of those areas. The variety of different areas of applications forces a very general setting. We are given a metric space X equipped with a doubling measure ¯. A generalization of a Sobolev function and its gradient is a pair u 2 L 1 loc (X), 0 g 2 L p (X) such that for every ball B ae X the Poincar'e-type inequality Z B ju \Gamma uB j d¯ Cr `Z oeB g p d¯ ' 1=p holds, where r is the radius of B and oe 1, C ? 0 are fixed constants. Working in the above setting we show that basically...

We consider the motion of a particle in a weak mean zero random force field F, which depends on the position, x(t), and the velocity, v(t) = 2(0. The equation of motion is 2(0 = ef(x(t), v(t), 0~), where x(') and v(-) take values in R d, d> 3, and co ranges over some probability space. We show, under suitable mixing and moment conditions on F, that as e--+ 0, v~(t)- v(t/e 2) converges weakly to a diffusion Markov process v(t), and e2x~(t) converges weakly to S v(s)ds + x, where x = lim e2x~(0).

Abstract. We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on multivariate interpolation polynomials associated with Schur’s S and P functions and with Jack symmetric functions. As a by–product, we compute certain Selberg–type integrals.

In a traditional structural model of default it is implicitly assumed that the information used to calibrate and run the model is publicly available. In reality, model inputs and parameters are unobservable. In this article we analyze the role of information in structural models, which we specify through a model definition of the default time and a model filtration. The model definition relates the default of a firm to its assets and liabilities. The model filtration describes the information of investors relative to the model definition. It parameterizes a family of default models for a given default time. An important situation is when the default is not observable with respect to the model filtration. Examples include models with incomplete information about firm assets and models with incomplete information about the liabilitydependent barrier that triggers default. Here the default time is typically totally inaccessible, as in the intensity-based, reduced-form models of default. In this case the model admits generalized reduced-form security pricing formulae in terms of the trend, which is the cumulative intensity. The trend can be explicitly characterized through the conditional default probability given the model filtration. If the trend is absolutely continuous with respect to the Lebesgue measure, then its density is the intensity and our formulae simplify to the classical

In our structural credit model based on incomplete information, investors cannot observe a firm’s default barrier. As a consequence, such a model has both the economic appeal of a structural model and the tractable pricing formulas and empirical plausibility of a reduced-form model. A comparison of default probability and credit spread forecasts generated by this model and two well-known structural models indicates that it reacts more quickly to new information and, unlike the other two models, it forecasts positive short-term credit spreads. Quantitative credit risk models have become central to the investment process in today’s very large and complex credit markets. There are

We consider direct sequence code division multiple access (DS-CDMA), modeling interference from users communicating with neighboring base stations by additive colored noise. We consider two types of receiver structures: first we consider the information-theoretically optimal receiver and use the sum capacity of the channel as our performance measure. Second, we consider the linear minimum mean square error (LMMSE) receiver and use the signal-to-interference ratio (SIR) of the estimate of the symbol transmitted as our performance measure. Our main result is a constructive characterization of the possible performance in both these scenarios. A central contribution of this characterization is the derivation of a qualitative feature of the optimal performance measure in both the scenarios studied. We show that the sum capacity is a saddle function:itisconvex in the additive noise covariances and concave in the user received powers. In the linear receiver case, we show that the minimum average power required to meet a set of target performance requirements of the users is a saddle function: it is convex in the additive noise covariances and concave in the set of performance requirements.

We present an introduction (also for non-experts) to a new framework for the analysis of (up to) second order differential operators (with merely measurable coefficients and in possibly infinitely many variables) on L²-spaces via associated bilinear forms. This new framework, in particular, covers both the elliptic and the parabolic case within one approach. To this end we introduce a new class of bilinear forms, so-called generalized Dirichlet forms, which are in general neither symmetric nor coercive, but still generate associated C0 --semigroups. Particular examples of generalized Dirichlet forms are symmetric and coercive Dirichlet forms (cf. [FOT], [MR1]) as well as time dependent Dirichlet forms (cf. [O1]). We discuss many applications to differential operators that can be treated within the new framework only, e.g. parabolic differential operators with unbounded drifts satisfying no L p --conditions, singular and fractional diffusion operators. Subsequently, we analyz...

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Abstract. We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition operator is explicitly diagonalizable with classical orthogonal polynomials as eigenfunctions. Key words and phrases: Gibbs sampler, running time analyses, exponential families, conjugate priors, location families, orthogonal polynomials, singular value decomposition. 1.