High Risk Scenarios And Extremesa Geometric Approach
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| Author | : A. A. Balkema |
| Publisher | : European Mathematical Society |
| Total Pages | : 398 |
| Release | : 2007 |
| Genre | : Business & Economics |
| ISBN | : 9783037190357 |
"Quantitative Risk Management (QRM) has become a field of research of considerable importance to numerous areas of application, including insurance, banking, energy, medicine, reliability. Mainly motivated by examples from insurance and finance, the authors develop a theory for handling multivariate extremes. The approach borrows ideas from portfolio theory and aims at an intuitive approach in the spirit of the Peaks over Thresholds method. The point of view is geometric. It leads to a probabilistic description of what in QRM language may be referred to as a high risk scenario: the conditional behaviour of risk factors given that a large move on a linear combination [portfolio, say] has been observed. The theoretical models which describe such conditional extremal behaviour are characterized and their relation to the limit theory for coordinatewise maxima is explained." "The book is based on a graduate course on point processes and extremes. It could form the basis for an advanced course on multivariate extreme value theory or a course on mathematical issues underlying risk. Students in statistics and finance with a mathematical, quantitative background are the prime audience. Actuaries and risk managers involved in data based risk analysis will find the models discussed in the book stimulating. The text contains many indications for further research."--BOOK JACKET.
| Author | : Piotr Jaworski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 299 |
| Release | : 2013-06-18 |
| Genre | : Business & Economics |
| ISBN | : 3642354076 |
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 1950s, copulas have gained considerable popularity in several fields of applied mathematics, especially finance and insurance. Today, copulas represent a well-recognized tool for market and credit models, aggregation of risks, and portfolio selection. Historically, the Gaussian copula model has been one of the most common models in credit risk. However, the recent financial crisis has underlined its limitations and drawbacks. In fact, despite their simplicity, Gaussian copula models severely underestimate the risk of the occurrence of joint extreme events. Recent theoretical investigations have put new tools for detecting and estimating dependence and risk (like tail dependence, time-varying models, etc) in the spotlight. All such investigations need to be further developed and promoted, a goal this book pursues. The book includes surveys that provide an up-to-date account of essential aspects of copula models in quantitative finance, as well as the extended versions of talks selected from papers presented at the workshop in Cracow.
| Author | : Bob Swarup |
| Publisher | : Bloomsbury Publishing |
| Total Pages | : 224 |
| Release | : 2012-05-24 |
| Genre | : Business & Economics |
| ISBN | : 1849300585 |
Effective asset-liability management (ALM) of a financial institution requires making informed strategic and operational decisions. Ever more important in the wake of the corporate bailouts and collapses of the financial crisis, ALM encompasses the formulation, implementation, monitoring, and revision of strategies, often on a daily basis due to the fast-moving nature of the related risks and constraints. This approachable book features up-to-date practitioner and academic perspectives to provide you with the knowledge you need. Key foundation information is backed up by the latest research and thought leadership to form a comprehensive guide to ALM for today and into the future, with case studies and worked examples. Detailed coverage includes: * Successful risk management frameworks * Coherent stress-testing * Modeling market risk * Derivatives and ALM * Contingency funding to manage liquidity risks * Basel III capital adequacy standard * Investment management for insurers * Property and casualty portfolio management * Funds transfer pricing * Problem loan modeling
| Author | : Alexander Lipton |
| Publisher | : OUP Oxford |
| Total Pages | : 704 |
| Release | : 2013-01-17 |
| Genre | : Business & Economics |
| ISBN | : 0191648248 |
From the late 1990s, the spectacular growth of a secondary market for credit through derivatives has been matched by the emergence of mathematical modelling analysing the credit risk embedded in these contracts. This book aims to provide a broad and deep overview of this modelling, covering statistical analysis and techniques, modelling of default of both single and multiple entities, counterparty risk, Gaussian and non-Gaussian modelling, and securitisation. Both reduced-form and firm-value models for the default of single entities are considered in detail, with extensive discussion of both their theoretical underpinnings and practical usage in pricing and risk. For multiple entity modelling, the now notorious Gaussian copula is discussed with analysis of its shortcomings, as well as a wide range of alternative approaches including multivariate extensions to both firm-value and reduced form models, and continuous-time Markov chains. One important case of multiple entities modelling - counterparty risk in credit derivatives - is further explored in two dedicated chapters. Alternative non-Gaussian approaches to modelling are also discussed, including extreme-value theory and saddle-point approximations to deal with tail risk. Finally, the recent growth in securitisation is covered, including house price modelling and pricing models for asset-backed CDOs. The current credit crisis has brought modelling of the previously arcane credit markets into the public arena. Lipton and Rennie with their excellent team of contributors, provide a timely discussion of the mathematical modelling that underpins both credit derivatives and securitisation. Though technical in nature, the pros and cons of various approaches attempt to provide a balanced view of the role that mathematical modelling plays in the modern credit markets. This book will appeal to students and researchers in statistics, economics, and finance, as well as practitioners, credit traders, and quantitative analysts
| Author | : Albert N. Shiryaev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 468 |
| Release | : 2013-01-09 |
| Genre | : Mathematics |
| ISBN | : 3642335497 |
The role of Yuri Vasilyevich Prokhorov as a prominent mathematician and leading expert in the theory of probability is well known. Even early in his career he obtained substantial results on the validity of the strong law of large numbers and on the estimates (bounds) of the rates of convergence, some of which are the best possible. His findings on limit theorems in metric spaces and particularly functional limit theorems are of exceptional importance. Y.V. Prokhorov developed an original approach to the proof of functional limit theorems, based on the weak convergence of finite dimensional distributions and the condition of tightness of probability measures. The present volume commemorates the 80th birthday of Yuri Vasilyevich Prokhorov. It includes scientific contributions written by his colleagues, friends and pupils, who would like to express their deep respect and sincerest admiration for him and his scientific work.
| Author | : Gareth W. Peters |
| Publisher | : John Wiley & Sons |
| Total Pages | : 656 |
| Release | : 2015-05-05 |
| Genre | : Mathematics |
| ISBN | : 1118909550 |
A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes in high consequence low frequency loss modeling. With a companion, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the book provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distributional approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modelling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The book is also a useful handbook for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.
| Author | : Erwan Faou |
| Publisher | : European Mathematical Society |
| Total Pages | : 152 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9783037191002 |
The goal of geometric numerical integration is the simulation of evolution equations possessing geometric properties over long periods of time. Of particular importance are Hamiltonian partial differential equations typically arising in application fields such as quantum mechanics or wave propagation phenomena. They exhibit many important dynamical features such as energy preservation and conservation of adiabatic invariants over long periods of time. In this setting, a natural question is how and to which extent the reproduction of such long-time qualitative behavior can be ensured by numerical schemes. Starting from numerical examples, these notes provide a detailed analysis of the Schrodinger equation in a simple setting (periodic boundary conditions, polynomial nonlinearities) approximated by symplectic splitting methods. Analysis of stability and instability phenomena induced by space and time discretization are given, and rigorous mathematical explanations are provided for them. The book grew out of a graduate-level course and is of interest to researchers and students seeking an introduction to the subject matter.
| Author | : Alexander J. McNeil |
| Publisher | : Princeton University Press |
| Total Pages | : 720 |
| Release | : 2015-05-26 |
| Genre | : Business & Economics |
| ISBN | : 0691166277 |
This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation
| Author | : Alexander H. W. Schmitt |
| Publisher | : European Mathematical Society |
| Total Pages | : 404 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9783037190654 |
The book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness of the number of quotients, and the variation of quotients. In the second part, GIT is applied to solve the classification problem of decorated principal bundles on a compact Riemann surface. The solution is a quasi-projective moduli scheme which parameterizes those objects that satisfy a semistability condition originating from gauge theory. The moduli space is equipped with a generalized Hitchin map. Via the universal Kobayashi-Hitchin correspondence, these moduli spaces are related to moduli spaces of solutions of certain vortex type equations. Potential applications include the study of representation spaces of the fundamental group of compact Riemann surfaces. The book concludes with a brief discussion of generalizations of these findings to higher dimensional base varieties, positive characteristic, and parabolic bundles. The text is fairly self-contained (e.g., the necessary background from the theory of principal bundles is included) and features numerous examples and exercises. It addresses students and researchers with a working knowledge of elementary algebraic geometry.
| Author | : Alain-Sol Sznitman |
| Publisher | : European Mathematical Society |
| Total Pages | : 128 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9783037191095 |
This book grew out of a graduate course at ETH Zurich during the spring 2011 term. It explores various links between such notions as occupation times of Markov chains, Gaussian free fields, Poisson point processes of Markovian loops, and random interlacements, which have been the object of intensive research over the last few years. These notions are developed in the convenient setup of finite weighted graphs endowed with killing measures. This book first discusses elements of continuous-time Markov chains, Dirichlet forms, potential theory, together with some consequences for Gaussian free fields. Next, isomorphism theorems and generalized Ray-Knight theorems, which relate occupation times of Markov chains to Gaussian free fields, are presented. Markovian loops are constructed and some of their key properties derived. The field of occupation times of Poisson point processes of Markovian loops is investigated. Of special interest are its connection to the Gaussian free field, and a formula of Symanzik. Finally, links between random interlacements and Markovian loops are discussed, and some further connections with Gaussian free fields are mentioned.
