The Fractional Ornstein-Uhlenbeck Process: Term Structure Theory and Application

The paper revisits dynamic term structure models (DTSMs) and proposes a new way in dealing with the limitation of the classical affine models. In particular, this paper expands the flexibility of the DTSMs by applying a fractional Brownian motion as the governing force of the state variable instead of the standard Brownian motion. This is a new direction in pricing non defaultable bonds with offspring in the arbitrage free pricing of weather derivatives based on fractional Brownian motions. By applying fractional Ito calculus and a fractional version of the Girsanov transform, a no arbitrage price of the bond is recovered by solving a fractional version of the fundamental bond pricing equation. Besides this theoretical contribution, the paper proposes an estimation methodology based on the Kalman filter approach, which is applied to the US term structure of interest rates.Fractional bond pricing equation; fractional Brownian motion; fractional Ornstein-Uhlenbeck process; long memory; Kalman filter

Management can be creative, too

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Estimating true age-dependence in survival when only adults can be observed: an example with Black-legged Kittiwakes

In long-lived birds, pre-breeders are often difficult or impossible to observe, and even though a proportion of marked adults may be of known age, the estimation of age-specific survival is complicated by the absence of observations during the first years of life. New developments in MARK now allow use of an updated individual covariate. We used this powerful approach to model age-dependence in survival of Black-legged Kittiwakes (Rissa tridactyla) at a North Sea colony. Although only 69 marked breeders were of known age, there was strong evidence for a quadratic relationship between true age and survival. We believe that this simple but powerful approach could be implemented for many species and could provide improved estimates of how survival changes with age, a central theme in life history theory

Cómo estimar el efecto real de la edad verdadera en la supervivencia cuando sólo es posible observar individuos adultos: ejemplo de la gaviota tridáctila

In long–lived birds, pre–breeders are often difficult or impossible to observe, and even though a proportion of marked adults may be of known age, the estimation of age–specific survival is complicated by the absence of observations during the first years of life. New developments in MARK now allow use of an updated individual covariate. We used this powerful approach to model age–dependence in survival of Black–legged Kittiwakes (Rissa tridactyla) at a North Sea colony. Although only 69 marked breeders were of known age, there was strong evidence for a quadratic relationship between true age and survival. We believe that this simple but powerful approach could be implemented for many species and could provide improved estimates of how survival changes with age, a central theme in life history theory.En las aves de larga vida, a menudo resulta difícil o incluso imposible observar individuos prerreproductores, y si bien un porcentaje de adultos marcados pueden ser de edad conocida, la estimación de la supervivencia a una edad específica se convierte en una tarea compleja, puesto que no se dispone de observaciones de los primeros años de vida. Las nuevas características del programa MARK nos permiten utilizar una covarianza individual actualizada. Empleamos este impactante enfoque para modelizar el efecto de la edad en la supervivencia de la gaviota tridáctila (Rissa tridactyla) en una colonia del mar del Norte. Aunque sólo 69 aves reproductoras marcadas eran de edad conocida, contábamos con numerosas pruebas que apuntaban a una relación cuadrática entre la edad real y la supervivencia. Creemos que este simple pero eficaz enfoque podría aplicarse en muchas especies, proporcionando estimaciones mejoradas acerca de cómo la supervivencia varía con la edad, un tema central de la teoría de las historias vitales

A technique for extracting potentially predictable patterns from climate data

We propose a computational technique which makes it possible to extract long-range potentially predictable patterns of interannual variability of meteorological seasonal mean fields. These patterns arise from slowly varying external forcing, such as sea surface temperatures, and slowly varying internal dynamics. The method provides a means of decomposing the covariance matrix of a seasonal mean field into covariance matrices for the potentially predictable and the chaotic, or weather-noise, components, separately. We illustrate the technique using Australian surface maximum temperatures during December-January-February (DJF) for the period 1958--1991. The dominant patterns, arising from the potentially predictable covariance matrix, are shown to be more closely related to slowly varying external forcing and slowly varying internal dynamics than those from a conventional analysis. The importance of tropical sea surface temperatures in forcing the potentially predictable patterns is also discussed

Particle Acceleration, Magnetic Field Generation, and Emission in Relativistic Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating into an ambient plasma. We find small differences in the results for no ambient and modest ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The small scale magnetic field structure generated by the Weibel instability is appropriate to the generation of ``jitter'' radiation from deflected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks.Comment: 6 pages, 1 figure, revised and accepted for Advances in Space Research (35th COSPAR Scientific Assembly, Paris, 18-25 July 2004

Nonlinear evolution of the magnetized Kelvin-Helmholtz instability: from fluid to kinetic modeling

The nonlinear evolution of collisionless plasmas is typically a multi-scale process where the energy is injected at large, fluid scales and dissipated at small, kinetic scales. Accurately modelling the global evolution requires to take into account the main micro-scale physical processes of interest. This is why comparison of different plasma models is today an imperative task aiming at understanding cross-scale processes in plasmas. We report here the first comparative study of the evolution of a magnetized shear flow, through a variety of different plasma models by using magnetohydrodynamic, Hall-MHD, two-fluid, hybrid kinetic and full kinetic codes. Kinetic relaxation effects are discussed to emphasize the need for kinetic equilibriums to study the dynamics of collisionless plasmas in non trivial configurations. Discrepancies between models are studied both in the linear and in the nonlinear regime of the magnetized Kelvin-Helmholtz instability, to highlight the effects of small scale processes on the nonlinear evolution of collisionless plasmas. We illustrate how the evolution of a magnetized shear flow depends on the relative orientation of the fluid vorticity with respect to the magnetic field direction during the linear evolution when kinetic effects are taken into account. Even if we found that small scale processes differ between the different models, we show that the feedback from small, kinetic scales to large, fluid scales is negligable in the nonlinear regime. This study show that the kinetic modeling validates the use of a fluid approach at large scales, which encourages the development and use of fluid codes to study the nonlinear evolution of magnetized fluid flows, even in the colisionless regime

Bayesian Error Estimation in Density Functional Theory

We present a practical scheme for performing error estimates for Density Functional Theory calculations. The approach which is based on ideas from Bayesian statistics involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities like binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.Comment: 5 pages, 3 figure

The Construction and Validation of an Arithmetical Computation Test

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67909/2/10.1177_001316445301300206.pd