### Financial Modeling Under Non-**Gaussian** Distributions

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Practitioners and researchers who have handled financial market data know that asset returns do not behave according to the bell-shaped curve, associated with the

**Gaussian**or normal distribution. Indeed, the use of**Gaussian**models when the asset return distributions are not normal could lead to a wrong choice of portfolio, the underestimation of extreme losses or mispriced derivative products. Consequently, non-**Gaussian**models and models based on processes with jumps, are gaining popularity among financial market practitioners. Non-**Gaussian**distributions are the key theme of this book which addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. One of the main aims is to bridge the gap between the theoretical developments and the practical implementations of what many users and researchers perceive as "sophisticated" models or black boxes. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series, such as exchange and interest rates. The authors have taken care to make the material accessible to anyone with a basic knowledge of statistics, calculus and probability, while at the same time preserving the mathematical rigor and complexity of the original models. This book will be an essential reference for practitioners in the finance industry, especially those responsible for managing portfolios and monitoring financial risk, but it will also be useful for mathematicians who want to know more about how their mathematical tools are applied in finance, and as a text for advanced courses in empirical finance; financial econometrics and financial derivatives.Category: Business. ISBN: 9781846284199

### Non-**Gaussian** Merton-Black-Scholes Theory

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This book introduces an analytically tractable and computationally effective class of non-

**Gaussian**models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton–Black–Scholes approach, which the authors call the Merton–Black–Scholes theory. The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-**Gaussian**situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further. Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics. Sample Chapter(s). Chapter 1.1: The**Gaussian**Merton-Black-Scholes theory (298 KB). Chapter 1.2: Regular Lévy Processes of Exponential type (271 KB). Chapter 1.3: Pricing of contingent claims (247 KB). Chapter 1.4: The Generalized Black-Scholes equation (207 KB). Chapter 1.5: Analytical methods used in the book (204 KB). Chapter 1.6: An overview of the results covered in the book (206 KB). Chapter 1.7: Commentary (112 KB). Contents: Lévy Processes; Regular Lévy Processes of Exponential Type in 1D; Pricing and Hedging of Contingent Claims of European Type; Perpetual American Options; American Options: Finite Time Horizon; First-Touch Digitals; Barrier Options; Multi-Asset Contracts; Investment Under Uncertainty and Capital Accumulation; Endogenous Default and Pricing of the Corporate Debt; Fast Pricing of European Options; Discrete Time Models; Feller Processes of Normal Inverse**Gaussian**Type; Pseudodifferential Operators with Constant Symbols; Elements of Calculus of Pseudodifferential Operators. Readership: Graduate students, researchers and academics in economics, mathematical finance, banking & finance/accounting; and financial engineers.Category: Business. ISBN: 9789810249441

### VaR Methodology for Non-**Gaussian** Finance

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With the impact of the recent financial crises, more attention must be given to new models in finance rejecting “Black-Scholes-Samuelson” assumptions leading to what is called non-

**Gaussian**finance. With the growing importance of Solvency II, Basel II and III regulatory rules for insurance companies and banks, value at risk (VaR) – one of the most popular risk indicator techniques plays a fundamental role in defining appropriate levels of equities. The aim of this book is to show how new VaR techniques can be built more appropriately for a crisis situation. VaR methodology for non-**Gaussian**finance looks at the importance of VaR in standard international rules for banks and insurance companies; gives the first non-**Gaussian**extensions of VaR and applies several basic statistical theories to extend classical results of VaR techniques such as the NP approximation, the Cornish-Fisher approximation, extreme and a Pareto distribution. Several non-**Gaussian**models using Copula methodology, Lévy processes along with particular attention to models with jumps such as the Merton model are presented; as are the consideration of time homogeneous and non-homogeneous Markov and semi-Markov processes and for each of these models. Contents 1. Use of Value-at-Risk (VaR) Techniques for Solvency II, Basel II and III. 2. Classical Value-at-Risk (VaR) Methods. 3. VaR Extensions from**Gaussian**Finance to Non-**Gaussian**Finance. 4. New VaR Methods of Non-**Gaussian**Finance. 5. Non-**Gaussian**Finance: Semi-Markov Models. About the Authors Marine Habart-Corlosquet is a Qualified and Certified Actuary at BNP Paribas Cardif, Paris, France. She is co-director of EURIA (Euro-Institut d’Actuariat, University of West Brittany, Brest, France), and associate researcher at Telecom Bretagne (Brest, France) as well as a board member of the French Institute of Actuaries. She teaches at EURIA, Telecom Bretagne and Ecole Centrale Paris (France). Her main research interests are pandemics, Solvency II internal models and ALM issues for insurance companies. Jacques Janssen is now Honorary Professor at the Solvay Business School (ULB) in Brussels, Belgium, having previously taught at EURIA (Euro-Institut d’Actuariat, University of West Brittany, Brest, France) and Telecom Bretagne (Brest, France) as well as being a director of Jacan Insurance and Finance Services, a consultancy and training company. Raimondo Manca is Professor of mathematical methods applied to economics, finance and actuarial science at University of Roma “La Sapienza” in Italy. He is associate editor for the journal Methodology and Computing in Applied Probability. His main research interests are multidimensional linear algebra, computational probability, application of stochastic processes to economics, finance and insurance and simulation models.Category: Business. ISBN: 9781848214644

### Stable Non-**Gaussian** Self-Similar Processes with Stationary Increments

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This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called deterministic flows. The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity. In-depth appendices are also included. This book is aimed at graduate students and researchers working in probability theory and statistics.

Category: Mathematics. ISBN: 9783319623306

### Handbook of Percentage Points of the Inverse **Gaussian** Distributions

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The purpose of this handbook is to provide comprehensive tables of percentage points of the inverse

**Gaussian**distribution. There is no other publication available today which condenses these tables - to such extent-in a concise, straightforward manner. The inverse**Gaussian**distribution is not only important for determining boundary crossing probabilities of Brownian Motion, which probabilities determine the operating characteristics of many sequential sampling procedures in statistics. It is also used in quality control procedures. This one-of-a-kind work includes a brief introductory section which outlines the inverse**Gaussian**distribution and explains the tables. The tables are produced in a fine grid of cumulative probabilities, and uses the closed form expression for the cumulative distribution function. This easy-to-use table reference also includes an excellent discussion of searching ordered tables. This handbook is a helpful, indispensable guide for all who are involved with statistics, mathematics, and computers. Mechanical engineers and physicists will find it useful also.Category: Medicine. ISBN: 9781315892061

### Electron Correlation in Molecules ab initio Beyond **Gaussian** Quantum Chemistry

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Electron Correlation in Molecules ab initio Beyond

**Gaussian**Quantum Chemistry presents a series of articles concerning important topics in quantum chemistry, including surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology Features detailed reviews written by leading international researchers The volume includes review on all the topics treated by world renown authors and cutting edge research contributions.Category: Science. ISBN: 9780128030608

### Handbook for Applied Modeling: Non-**Gaussian** and Correlated Data

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This compact, entry-level Handbook equips applied practitioners to choose and use core models for real-world data - with R and SAS.

Category: Business. ISBN: 9781107146990

### Modelling and Control of Dynamic Systems Using **Gaussian** Process Models

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This monograph opens up new horizons for engineers and researchers inacademia and in industry dealing with or interested in new developments in thefield of system identification and control. It emphasizes guidelines forworking solutions and practical advice for their implementation rather than thetheoretical background of

**Gaussian**process (GP) models. The book demonstratesthe potential of this recent development in probabilistic machine-learningmethods and gives the reader an intuitive understanding of the topic. Thecurrent state of the art is treated along with possible future directions forresearch. Systems control design relies on mathematical models and these may bedeveloped from measurement data. This process of system identification, whenbased on GP models, can play an integral part of control design in data-basedcontrol and its description as such is an essential aspect of the text. Thebackground of GP regression is introduced first with system identification andincorporation of prior knowledge then leading into full-blown control. The bookis illustrated by extensive use of examples, line drawings, and graphicalpresentation of computer-simulation results and plant measurements. Theresearch results presented are applied in real-life case studies drawn fromsuccessful applications including: a gasliquid separator control; urban-traffic signal modelling and reconstruction; and prediction of atmospheric ozone concentration. A MATLAB toolbox, for identification and simulation ofdynamic GP models is provided for download.Category: Technology. ISBN: 9783319210209

### Stochastic Analysis for **Gaussian** Random Processes and Fields

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Stochastic Analysis for

**Gaussian**Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it studies**Gaussian**random fields using reproducing kernel Hilbert spaces (RKHSs). The book begins with preliminary results on covariance and associated RKHS before introducing the**Gaussian**process and**Gaussian**random fields. The authors use chaos expansion to define the Skorokhod integral, which generalizes the It integral. They show how the Skorokhod integral is a dual operator of Skorokhod differentiation and the divergence operator of Malliavin. The authors also present**Gaussian**processes indexed by real numbers and obtain a KallianpurStriebel Bayes' formula for the filtering problem. After discussing the problem of equivalence and singularity of**Gaussian**random fields (including a generalization of the Girsanov theorem), the book concludes with the Markov property of**Gaussian**random fields indexed by measures and generalized**Gaussian**random fields indexed by Schwartz space. The Markov property for generalized random fields is connected to the Markov process generated by a Dirichlet form.Category: Mathematics. ISBN: 9781498707817

### Detection of Random Signals in Dependent **Gaussian** Noise

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The book presents the necessary mathematical basis to obtain and rigorously use likelihoods for detection problems with

**Gaussian**noise. To facilitate comprehension the text is divided into three broad areas reproducing kernel Hilbert spaces, Cramr-Hida representations and stochastic calculus for which a somewhat different approach was used than in their usual stand-alone context. One main applicable result of the book involves arriving at a general solution to the canonical detection problem for active sonar in a reverberation-limited environment. Nonetheless, the general problems dealt with in the text also provide a useful framework for discussing other current research areas, such as wavelet decompositions, neural networks, and higher order spectral analysis. The structure of the book, with the exposition presenting as many details as necessary, was chosen to serve both those readers who are chiefly interested in the results and those who want to learn the material from scratch. Hence, the text will be useful for graduate students and researchers alike in the fields of engineering, mathematics and statistics.Category: Mathematics. ISBN: 9783319223148