High Risk Scenarios And Extremes A Geometric Approach

Author : A. A. Balkema,Paul Embrechts
Publisher : European Mathematical Society
Page : 398 pages
File Size : 43,6 Mb
Release : 2007
Category : Business & Economics
ISBN : 3037190353

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High Risk Scenarios and Extremes by A. A. Balkema,Paul Embrechts Pdf

"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 : GUUS BALKEMA; PAUL EMBRECHTS.
Publisher : Unknown
Page : 128 pages
File Size : 47,9 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 3037195355

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HIGH RISK SCENARIOS AND EXTREMES;A GEOMETRIC APPROACH. by GUUS BALKEMA; PAUL EMBRECHTS. Pdf

Author : Bob Swarup
Publisher : Bloomsbury Publishing
Page : 224 pages
File Size : 53,6 Mb
Release : 2012-05-24
Category : Business & Economics
ISBN : 9781849300582

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Asset–Liability Management for Financial Institutions by Bob Swarup Pdf

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 : Piotr Jaworski,Fabrizio Durante,Wolfgang Karl Härdle
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 54,8 Mb
Release : 2013-06-18
Category : Business & Economics
ISBN : 9783642354076

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Copulae in Mathematical and Quantitative Finance by Piotr Jaworski,Fabrizio Durante,Wolfgang Karl Härdle Pdf

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 : Gareth W. Peters,Pavel V. Shevchenko
Publisher : John Wiley & Sons
Page : 656 pages
File Size : 46,6 Mb
Release : 2015-05-05
Category : Mathematics
ISBN : 9781118909553

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Advances in Heavy Tailed Risk Modeling by Gareth W. Peters,Pavel V. Shevchenko Pdf

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 : Alexander Lipton,Andrew Rennie
Publisher : OUP Oxford
Page : 704 pages
File Size : 40,6 Mb
Release : 2013-01-17
Category : Business & Economics
ISBN : 9780191648250

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The Oxford Handbook of Credit Derivatives by Alexander Lipton,Andrew Rennie Pdf

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 : Erwan Faou
Publisher : European Mathematical Society
Page : 152 pages
File Size : 49,6 Mb
Release : 2012
Category : Numerical integration
ISBN : 3037191007

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Geometric Numerical Integration and Schrödinger Equations by Erwan Faou Pdf

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,Rüdiger Frey,Paul Embrechts
Publisher : Princeton University Press
Page : 720 pages
File Size : 49,7 Mb
Release : 2015-05-26
Category : Business & Economics
ISBN : 9780691166278

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Quantitative Risk Management by Alexander J. McNeil,Rüdiger Frey,Paul Embrechts Pdf

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
Page : 404 pages
File Size : 43,7 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190655

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Geometric Invariant Theory and Decorated Principal Bundles by Alexander H. W. Schmitt Pdf

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 : Barrieu Pauline
Publisher : World Scientific
Page : 320 pages
File Size : 42,6 Mb
Release : 2019-04-18
Category : Business & Economics
ISBN : 9781786341969

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Risk And Stochastics: Ragnar Norberg by Barrieu Pauline Pdf

with an autobiography from Ragnar NorbergThe Risk and Stochastics Conference, held at the Royal Statistical Society in April 2015, brought together academics from the worlds of actuarial science, stochastic calculus, finance and statistics to celebrate the achievements of Professor Ragnar Norberg as he turned 70. After the conference, Ragnar Norberg suddenly fell very ill and passed away; this book honours his life and work.This collection of articles is written by speakers of the conference, themselves respected academics who have influenced and been influenced by the life and work of Professor Norberg. His professional and academic achievements are celebrated here, most significantly the instrumental work he put into setting up the world-renowned Risk and Stochastics Enterprise at the London School of Economics (LSE). Subjects covered include discussion of risk measurements, ruin constraint, supporting stable pensions, filtration in discrete time, Riesz means and Beurling moving averages and orthonormal polynomial expansions. Also featured are notes from contributors giving account of their personal relations with Professor Norberg, as well as an autobiographical chapter from the man himself.Aimed at graduate level students and researchers interested in the life and work of Ragnar Norberg, this book provides a unique opportunity to reflect on and understand key findings and ground-breaking research in modern actuarial and financial mathematics and their interface, while giving intimate insights into the life of a leading academic mind.

Author : Alain-Sol Sznitman
Publisher : European Mathematical Society
Page : 128 pages
File Size : 45,6 Mb
Release : 2012
Category : Gaussian processes
ISBN : 3037191090

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Topics in Occupation Times and Gaussian Free Fields by Alain-Sol Sznitman Pdf

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.

Author : Kenji Nakanishi,Wilhelm Schlag
Publisher : European Mathematical Society
Page : 264 pages
File Size : 43,9 Mb
Release : 2011
Category : Hamiltonian systems
ISBN : 3037190957

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Invariant Manifolds and Dispersive Hamiltonian Evolution Equations by Kenji Nakanishi,Wilhelm Schlag Pdf

The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein-Gordon and Schrodinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter. One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface which separates a region of finite-time blowup in forward time from one which exhibits global existence and scattering to zero in forward time. The authors' entire analysis takes place in the energy topology, and the conserved energy can exceed the ground state energy only by a small amount. This monograph is based on recent research by the authors. The proofs rely on an interplay between the variational structure of the ground states and the nonlinear hyperbolic dynamics near these states. A key element in the proof is a virial-type argument excluding almost homoclinic orbits originating near the ground states, and returning to them, possibly after a long excursion. These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein-Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle.

Author : Paul Seidel
Publisher : European Mathematical Society
Page : 340 pages
File Size : 41,9 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190639

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Fukaya Categories and Picard-Lefschetz Theory by Paul Seidel Pdf

The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry.

Author : Camillo De Lellis
Publisher : European Mathematical Society
Page : 140 pages
File Size : 55,8 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190442

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Rectifiable Sets, Densities and Tangent Measures by Camillo De Lellis Pdf

The characterization of rectifiable sets through the existence of densities is a pearl of geometric measure theory. The difficult proof, due to Preiss, relies on many beautiful and deep ideas and novel techniques. Some of them have already proven useful in other contexts, whereas others have not yet been exploited. These notes give a simple and short presentation of the former and provide some perspective of the latter. This text emerged from a course on rectifiability given at the University of Zurich. It is addressed both to researchers and students; the only prerequisite is a solid knowledge in standard measure theory. The first four chapters give an introduction to rectifiable sets and measures in Euclidean spaces, covering classical topics such as the area formula, the theorem of Marstrand and the most elementary rectifiability criterions. The fifth chapter is dedicated to a subtle rectifiability criterion due to Marstrand and generalized by Mattila, and the last three focus on Preiss' result. The aim is to provide a self-contained reference for anyone interested in an overview of this fascinating topic.

Author : Michael Farber
Publisher : European Mathematical Society
Page : 148 pages
File Size : 52,5 Mb
Release : 2008
Category : Mathematics
ISBN : 303719054X

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Invitation to Topological Robotics by Michael Farber Pdf

This book discusses several selected topics of a new emerging area of research on the interface between topology and engineering. The first main topic is topology of configuration spaces of mechanical linkages. These manifolds arise in various fields of mathematics and in other sciences, e.g., engineering, statistics, molecular biology. To compute Betti numbers of these configuration spaces the author applies a new technique of Morse theory in the presence of an involution. A significant result of topology of linkages presented in this book is a solution of a conjecture of Kevin Walker which states that the relative sizes of bars of a linkage are determined, up to certain equivalence, by the cohomology algebra of the linkage configuration space. This book also describes a new probabilistic approach to topology of linkages which treats the bar lengths as random variables and studies mathematical expectations of Betti numbers. The second main topic is topology of configuration spaces associated to polyhedra. The author gives an account of a beautiful work of S. R. Gal, suggesting an explicit formula for the generating function encoding Euler characteristics of these spaces. Next the author studies the knot theory of a robot arm, focusing on a recent important result of R. Connelly, E. Demain, and G. Rote. Finally, he investigates topological problems arising in the theory of robot motion planning algorithms and studies the homotopy invariant TC(X) measuring navigational complexity of configuration spaces. This book is intended as an appetizer and will introduce the reader to many fascinating topological problems motivated by engineering.