Discrete Time Asset Pricing Models In Applied Stochastic Finance
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Discrete Time Asset Pricing Models In Applied Stochastic Finance
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Author : P. C. G. Vassiliou
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-01
Discrete Time Asset Pricing Models In Applied Stochastic Finance written by P. C. G. Vassiliou and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-01 with Mathematics categories.
Stochastic finance and financial engineering have been rapidly expanding fields of science over the past four decades, mainly due to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better comprehending, modeling and hedging this kind of risk. These two volumes aim to provide a foundation course on applied stochastic finance. They are designed for three groups of readers: firstly, students of various backgrounds seeking a core knowledge on the subject of stochastic finance; secondly financial analysts and practitioners in the investment, banking and insurance industries; and finally other professionals who are interested in learning advanced mathematical and stochastic methods, which are basic knowledge in many areas, through finance. Volume 1 starts with the introduction of the basic financial instruments and the fundamental principles of financial modeling and arbitrage valuation of derivatives. Next, we use the discrete-time binomial model to introduce all relevant concepts. The mathematical simplicity of the binomial model also provides us with the opportunity to introduce and discuss in depth concepts such as conditional expectations and martingales in discrete time. However, we do not expand beyond the needs of the stochastic finance framework. Numerous examples, each highlighted and isolated from the text for easy reference and identification, are included. The book concludes with the use of the binomial model to introduce interest rate models and the use of the Markov chain model to introduce credit risk. This volume is designed in such a way that, among other uses, makes it useful as an undergraduate course.
Banach Fr Chet Hilbert And Neumann Spaces
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Author : Jacques Simon
language : en
Publisher: John Wiley & Sons
Release Date : 2017-06-26
Banach Fr Chet Hilbert And Neumann Spaces written by Jacques Simon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-26 with Mathematics categories.
This book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics. Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fréchet and Hilbert, with new developments on Neumann spaces, but also on extractable spaces. The author presents the main properties of these spaces, which are useful for the construction of Lebesgue and Sobolev distributions with real or vector values and for solving partial differential equations. Differential calculus is also extended to semi-normed spaces. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers without restricting or generalizing the results.
Stochastic Modeling And Optimization Methods For Critical Infrastructure Protection Volume 2
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Author : Alexei A. Gaivoronski
language : en
Publisher: John Wiley & Sons
Release Date : 2025-05-13
Stochastic Modeling And Optimization Methods For Critical Infrastructure Protection Volume 2 written by Alexei A. Gaivoronski and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-13 with Business & Economics categories.
Stochastic Modeling and Optimization Methods for Critical Infrastructure Protection is a thorough exploration of mathematical models and tools that are designed to strengthen critical infrastructures against threats – both natural and adversarial. Divided into two volumes, this first volume examines stochastic modeling across key economic sectors and their interconnections, while the second volume focuses on advanced mathematical methods for enhancing infrastructure protection. The book covers a range of themes, including risk assessment techniques that account for systemic interdependencies within modern technospheres, the dynamics of uncertainty, instability and system vulnerabilities. The book also presents other topics such as cryptographic information protection and Shannon’s theory of secret systems, alongside solutions arising from optimization, game theory and machine learning approaches. Featuring research from international collaborations, this book covers both theory and applications, offering vital insights for advanced risk management curricula. It is intended not only for researchers, but also educators and professionals in infrastructure protection and stochastic optimization.
Statistical Inference For Piecewise Deterministic Markov Processes
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Author : Romain Azais
language : en
Publisher: John Wiley & Sons
Release Date : 2018-07-30
Statistical Inference For Piecewise Deterministic Markov Processes written by Romain Azais and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-30 with Mathematics categories.
Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance... Such processes are defined by a deterministic motion punctuated by random jumps at random times, and offer simple yet challenging models to study. Nevertheless, the issue of statistical estimation of the parameters ruling the jump mechanism is far from trivial. Responding to new developments in the field as well as to current research interests and needs, Statistical inference for piecewise-deterministic Markov processes offers a detailed and comprehensive survey of state-of-the-art results. It covers a wide range of general processes as well as applied models. The present book also dwells on statistics in the context of Markov chains, since piecewise-deterministic Markov processes are characterized by an embedded Markov chain corresponding to the position of the process right after the jumps.
Earthquake Occurrence
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Author : Rodolfo Console
language : en
Publisher: John Wiley & Sons
Release Date : 2017-08-07
Earthquake Occurrence written by Rodolfo Console and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-07 with Mathematics categories.
Earthquake Occurrence provides the reader with a review of algorithms applicable for modeling seismicity, such as short-term earthquake clustering and pseudo-periodic long-term behavior of major earthquakes. The concept of the likelihood ratio of a set of observations under different hypotheses is applied for comparison among various models. In short-term models, known by the term ETAS, the occurrence space and time rate density of earthquakes is modeled as the sum of two terms, one representing the independent or spontaneous events, and the other representing the activity triggered by previous earthquakes. Examples of the application of such algorithms in real cases are also reported. Dealing with long-term recurrence models, renewal time-dependent models, implying a pseudo-periodicity of earthquake occurrence, are compared with the simple time-independent Poisson model, in which every event occurs regardless of what has occurred in the past. The book also introduces a number of computer codes developed by the authors over decades of seismological research.
Fat Tailed Distributions
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Author : Roger M. Cooke
language : en
Publisher: John Wiley & Sons
Release Date : 2014-11-11
Fat Tailed Distributions written by Roger M. Cooke and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-11 with Mathematics categories.
This title is written for the numerate nonspecialist, and hopes to serve three purposes. First it gathers mathematical material from diverse but related fields of order statistics, records, extreme value theory, majorization, regular variation and subexponentiality. All of these are relevant for understanding fat tails, but they are not, to our knowledge, brought together in a single source for the target readership. Proofs that give insight are included, but for most fussy calculations the reader is referred to the excellent sources referenced in the text. Multivariate extremes are not treated. This allows us to present material spread over hundreds of pages in specialist texts in twenty pages. Chapter 5 develops new material on heavy tail diagnostics and gives more mathematical detail. Since variances and covariances may not exist for heavy tailed joint distributions, Chapter 6 reviews dependence concepts for certain classes of heavy tailed joint distributions, with a view to regressing heavy tailed variables. Second, it presents a new measure of obesity. The most popular definitions in terms of regular variation and subexponentiality invoke putative properties that hold at infinity, and this complicates any empirical estimate. Each definition captures some but not all of the intuitions associated with tail heaviness. Chapter 5 studies two candidate indices of tail heaviness based on the tendency of the mean excess plot to collapse as data are aggregated. The probability that the largest value is more than twice the second largest has intuitive appeal but its estimator has very poor accuracy. The Obesity index is defined for a positive random variable X as: Ob(X) = P (X1 +X4 > X2 +X3|X1 ≤ X2 ≤ X3 ≤ X4), Xi independent copies of X. For empirical distributions, obesity is defined by bootstrapping. This index reasonably captures intuitions of tail heaviness. Among its properties, if α > 1 then Ob(X) Ob(Xα). However, it does not completely mimic the tail index of regularly varying distributions, or the extreme value index. A Weibull distribution with shape 1/4 is more obese than a Pareto distribution with tail index 1, even though this Pareto has infinite mean and the Weibull’s moments are all finite. Chapter 5 explores properties of the Obesity index. Third and most important, we hope to convince the reader that fat tail phenomena pose real problems; they are really out there and they seriously challenge our usual ways of thinking about historical averages, outliers, trends, regression coefficients and confidence bounds among many other things. Data on flood insurance claims, crop loss claims, hospital discharge bills, precipitation and damages and fatalities from natural catastrophes drive this point home. While most fat tailed distributions are ”bad”, research in fat tails is one distribution whose tail will hopefully get fatter.
Integrable Systems
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Author : Ahmed Lesfari
language : en
Publisher: John Wiley & Sons
Release Date : 2022-07-13
Integrable Systems written by Ahmed Lesfari and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-13 with Mathematics categories.
This book illustrates the powerful interplay between topological, algebraic and complex analytical methods, within the field of integrable systems, by addressing several theoretical and practical aspects. Contemporary integrability results, discovered in the last few decades, are used within different areas of mathematics and physics. Integrable Systems incorporates numerous concrete examples and exercises, and covers a wealth of essential material, using a concise yet instructive approach. This book is intended for a broad audience, ranging from mathematicians and physicists to students pursuing graduate, Masters or further degrees in mathematics and mathematical physics. It also serves as an excellent guide to more advanced and detailed reading in this fundamental area of both classical and contemporary mathematics.
Dynamics Of Statistical Experiments
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Author : Dmitri Koroliouk
language : en
Publisher: John Wiley & Sons
Release Date : 2020-06-03
Dynamics Of Statistical Experiments written by Dmitri Koroliouk and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-03 with Mathematics categories.
This book is devoted to the system analysis of statistical experiments, determined by the averaged sums of sampling random variables. The dynamics of statistical experiments are given by difference stochastic equations with a speci?ed regression function of increments linear or nonlinear. The statistical experiments are studied by the sample volume increasing (N ??), as well as in discrete-continuous time by the number of stages increasing (k ??) for different conditions imposed on the regression function of increments. The proofs of limit theorems employ modern methods for the operator and martingale characterization of Markov processes, including singular perturbation methods. Furthermore, they justify the representation of a stationary Gaussian statistical experiment with the Markov property, as a stochastic difference equation solution, applying the theorem of normal correlation. The statistical hypotheses verification problem is formulated in the classification of evolutionary processes, which determine the dynamics of the predictable component. The method of stochastic approximation is used for classifying statistical experiments.
Gaussian Measures In Hilbert Space
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Author : Alexander Kukush
language : en
Publisher: John Wiley & Sons
Release Date : 2020-02-26
Gaussian Measures In Hilbert Space written by Alexander Kukush and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-26 with Mathematics categories.
At the nexus of probability theory, geometry and statistics, a Gaussian measure is constructed on a Hilbert space in two ways: as a product measure and via a characteristic functional based on Minlos-Sazonov theorem. As such, it can be utilized for obtaining results for topological vector spaces. Gaussian Measures contains the proof for Ferniques theorem and its relation to exponential moments in Banach space. Furthermore, the fundamental Feldman-Hájek dichotomy for Gaussian measures in Hilbert space is investigated. Applications in statistics are also outlined. In addition to chapters devoted to measure theory, this book highlights problems related to Gaussian measures in Hilbert and Banach spaces. Borel probability measures are also addressed, with properties of characteristic functionals examined and a proof given based on the classical Banach Steinhaus theorem. Gaussian Measures is suitable for graduate students, plus advanced undergraduate students in mathematics and statistics. It is also of interest to students in related fields from other disciplines. Results are presented as lemmas, theorems and corollaries, while all statements are proven. Each subsection ends with teaching problems, and a separate chapter contains detailed solutions to all the problems. With its student-tested approach, this book is a superb introduction to the theory of Gaussian measures on infinite-dimensional spaces.
From Euclidean To Hilbert Spaces
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Author : Edoardo Provenzi
language : en
Publisher: John Wiley & Sons
Release Date : 2021-08-03
From Euclidean To Hilbert Spaces written by Edoardo Provenzi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-03 with Mathematics categories.
From Euclidian to Hilbert Spaces analyzes the transition from finite dimensional Euclidian spaces to infinite-dimensional Hilbert spaces, a notion that can sometimes be difficult for non-specialists to grasp. The focus is on the parallels and differences between the properties of the finite and infinite dimensions, noting the fundamental importance of coherence between the algebraic and topological structure, which makes Hilbert spaces the infinite-dimensional objects most closely related to Euclidian spaces. The common thread of this book is the Fourier transform, which is examined starting from the discrete Fourier transform (DFT), along with its applications in signal and image processing, passing through the Fourier series and finishing with the use of the Fourier transform to solve differential equations. The geometric structure of Hilbert spaces and the most significant properties of bounded linear operators in these spaces are also covered extensively. The theorems are presented with detailed proofs as well as meticulously explained exercises and solutions, with the aim of illustrating the variety of applications of the theoretical results.