Infinite Dimensional Affine Term Structure Models Under Incomplete Information PDF Download
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Languages : en
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Languages : en
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Author: Weijun Yu
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Languages : en
Pages :
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Abstract: The first part of the dissertation extends some important results in the classical theory of finite dimensional affine processes to infinite dimensional separable Hilbert spaces. In particular, a necessary and sufficient condition for a continuous Markov diffusion process to be affine is given. Based on the extended theory, two affine term structure models are introduced and the existence and uniqueness of the two models are studied. The second part concentrates on a non-linear filtering problem with infinite dimensional observations and the Kushner-Stratonovich equation under the infinite dimensional observation setting is derived. Finally, the obtained results are applied to study the Kalman-Bucy filter with infinite dimensional observations. It is proved that the filter has a Gaussian distribution and the evolution equations of the mean and the covariance of the filter are deduced from the Kushner-Stratonovich equation
Author: Rama Cont
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Languages : en
Pages : 0
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Author: Christian Gouriéroux
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Category :
Languages : en
Pages : 66
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Author: G. Constantinides
Publisher: Elsevier
ISBN: 0080495087
Category : Business & Economics
Languages : en
Pages : 698
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Volume 1B covers the economics of financial markets: the saving and investment decisions; the valuation of equities, derivatives, and fixed income securities; and market microstructure.
Author: Jan Baldeaux
Publisher: Springer Science & Business Media
ISBN: 3319007475
Category : Mathematics
Languages : en
Pages : 432
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Book Description
This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.
Author: Damir Filipovic
Publisher: Springer Science & Business Media
ISBN: 3540680152
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.
Author:
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Category : Mathematics
Languages : en
Pages : 1052
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Author: Boris Zilber
Publisher: American Mathematical Soc.
ISBN: 9780821897454
Category : Mathematics
Languages : en
Pages : 132
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Book Description
The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories , this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.
Author: Darrell Duffie
Publisher: Princeton University Press
ISBN: 1400829208
Category : Business & Economics
Languages : en
Pages : 488
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Book Description
This is a thoroughly updated edition of Dynamic Asset Pricing Theory, the standard text for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis, so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. Readers will be particularly intrigued by this latest edition's most significant new feature: a chapter on corporate securities that offers alternative approaches to the valuation of corporate debt. Also, while much of the continuous-time portion of the theory is based on Brownian motion, this third edition introduces jumps--for example, those associated with Poisson arrivals--in order to accommodate surprise events such as bond defaults. Applications include term-structure models, derivative valuation, and hedging methods. Numerical methods covered include Monte Carlo simulation and finite-difference solutions for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. A system of appendixes reviews the necessary mathematical concepts. And references have been updated throughout. With this new edition, Dynamic Asset Pricing Theory remains at the head of the field.
