Download or read book Applications of Asymptotic Methods in Quantitative Finance and Insurance written by Amogh Deshpande and published by . This book was released on 2014 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Large Deviations and Asymptotic Methods in Finance written by Peter K. Friz and published by Springer. This book was released on 2015-06-16 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.
Download or read book Introduction to Asymptotic Methods written by David Y Gao and published by CRC Press. This book was released on 2019-08-30 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important methods of singular perturbations within the scope of application of differential equations. The authors take a challenging and original approach based on the integrated mathematical-analytical treatment of various objects taken from interdisciplinary fields of mechanics, physics, and applied mathematics. This new hybrid approach will lead to results that cannot be obtained by standard theories in the field. Emphasizing fundamental elements of the mathematical modeling process, the book provides comprehensive coverage of asymptotic approaches, regular and singular perturbations, one-dimensional non-stationary non-linear waves, Padé approximations, oscillators with negative Duffing type stiffness, and differential equations with discontinuous nonlinearities. The book also offers a method of construction for canonical variables transformation in parametric form along with a number of examples and applications. The book is applications oriented and features results and literature citations that have not been seen in the Western Scientific Community. The authors emphasize the dynamics of the development of perturbation methods and present the development of ideas associated with this wide field of research.
Download or read book Statistical Inference in Financial and Insurance Mathematics with R written by Alexandre Brouste and published by Elsevier. This book was released on 2017-11-22 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finance and insurance companies are facing a wide range of parametric statistical problems. Statistical experiments generated by a sample of independent and identically distributed random variables are frequent and well understood, especially those consisting of probability measures of an exponential type. However, the aforementioned applications also offer non-classical experiments implying observation samples of independent but not identically distributed random variables or even dependent random variables. Three examples of such experiments are treated in this book. First, the Generalized Linear Models are studied. They extend the standard regression model to non-Gaussian distributions. Statistical experiments with Markov chains are considered next. Finally, various statistical experiments generated by fractional Gaussian noise are also described. In this book, asymptotic properties of several sequences of estimators are detailed. The notion of asymptotical efficiency is discussed for the different statistical experiments considered in order to give the proper sense of estimation risk. Eighty examples and computations with R software are given throughout the text. Examines a range of statistical inference methods in the context of finance and insurance applications Presents the LAN (local asymptotic normality) property of likelihoods Combines the proofs of LAN property for different statistical experiments that appears in financial and insurance mathematics Provides the proper description of such statistical experiments and invites readers to seek optimal estimators (performed in R) for such statistical experiments
Download or read book Modelling Extremal Events written by Paul Embrechts and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A reader's first impression on leafing through this book is of the large number of graphs and diagrams, used to illustrate shapes of distributions...and to show real data examples in various ways. A closer reading reveals a nice mix of theory and applications, with the copious graphical illustrations alluded to. Such a mixture is of course dear to the heart of the applied probabilist/statistician, and should impress even the most ardent theorists." --MATHEMATICAL REVIEWS
Download or read book Asymptotic Methods in Probability and Statistics with Applications written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditions of the 150-year-old St. Petersburg School of Probability and Statis tics had been developed by many prominent scientists including P. L. Cheby chev, A. M. Lyapunov, A. A. Markov, S. N. Bernstein, and Yu. V. Linnik. In 1948, the Chair of Probability and Statistics was established at the Department of Mathematics and Mechanics of the St. Petersburg State University with Yu. V. Linik being its founder and also the first Chair. Nowadays, alumni of this Chair are spread around Russia, Lithuania, France, Germany, Sweden, China, the United States, and Canada. The fiftieth anniversary of this Chair was celebrated by an International Conference, which was held in St. Petersburg from June 24-28, 1998. More than 125 probabilists and statisticians from 18 countries (Azerbaijan, Canada, Finland, France, Germany, Hungary, Israel, Italy, Lithuania, The Netherlands, Norway, Poland, Russia, Taiwan, Turkey, Ukraine, Uzbekistan, and the United States) participated in this International Conference in order to discuss the current state and perspectives of Probability and Mathematical Statistics. The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches. The main theme of the Conference was chosen in the tradition of the St.
Download or read book Asymptotic Theory in Probability and Statistics with Applications written by T. L. Lai and published by . This book was released on 2008 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is suitable for graduate students in probability and statistics.
Download or read book Generalized Poisson Models and Their Applications in Insurance and Finance written by Vladimir E. Bening and published by VSP. This book was released on 2002-01-01 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the "Modern Probability and Statistics series aims to fill the gap in existing literature on compound Cox processes, i.e. sums of independent identically distributed random variables up to a doubly stochastic Poisson process, which are very important, especially for insurance and financial applications where they provide good asymptotic approximations for basic characteristics such as the distributions of the surplus of an insurance company under risk and portfolio fluctuations or of increments of stock prices under non-constant intensity of trade. It presents the present state-of-the-art in the field of compound Cox processes and their applications in insurance and finance. Besides a review of well-known classical results on compound and mixed Poisson processes and risk theory, it contains many new, recently obtained results by the authors. Among these are: new convergence criteria, convergence rate estimates, asymptotic expansions for quantiles of stochastic processes and many others. From the applied problems considered in this book, four deserve to be mentioned especially: 1) modelling the distribution of increments of stock prices, closely connected with prediction of the behaviour of financial indexes; 2) the description of asymptotic behaviour of the so-called generalized risk processes, which take into account both risk and portfolio fluctuations; 3) statistical estimation of the probability of ruin for a generalized risk process; 4) construction of refined approximations to the ruin probability, based on its asymptotic expansions with small safety loading. This book will be of great value to specialists in applied probability and to those who use modelsand methods of probability theory to solve practical problems in the fields of insurance and finance.
Download or read book Mathematical and Statistical Methods for Insurance and Finance written by Cira Perna and published by Springer Science & Business Media. This book was released on 2007-12-12 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interaction between mathematicians and statisticians reveals to be an effective approach to the analysis of insurance and financial problems, in particular in an operative perspective. The Maf2006 conference, held at the University of Salerno in 2006, had precisely this purpose and the collection published here gathers some of the papers presented at the conference and successively worked out to this aim. They cover a wide variety of subjects in insurance and financial fields.
Download or read book Financial and Actuarial Statistics written by Dale S. Borowiak and published by CRC Press. This book was released on 2013-11-12 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understand Up-to-Date Statistical Techniques for Financial and Actuarial Applications Since the first edition was published, statistical techniques, such as reliability measurement, simulation, regression, and Markov chain modeling, have become more prominent in the financial and actuarial industries. Consequently, practitioners and students must acquire strong mathematical and statistical backgrounds in order to have successful careers. Financial and Actuarial Statistics: An Introduction, Second Edition enables readers to obtain the necessary mathematical and statistical background. It also advances the application and theory of statistics in modern financial and actuarial modeling. Like its predecessor, this second edition considers financial and actuarial modeling from a statistical point of view while adding a substantial amount of new material. New to the Second Edition Nomenclature and notations standard to the actuarial field Excel exercises with solutions, which demonstrate how to use Excel functions for statistical and actuarial computations Problems dealing with standard probability and statistics theory, along with detailed equation links A chapter on Markov chains and actuarial applications Expanded discussions of simulation techniques and applications, such as investment pricing Sections on the maximum likelihood approach to parameter estimation as well as asymptotic applications Discussions of diagnostic procedures for nonnegative random variables and Pareto, lognormal, Weibull, and left truncated distributions Expanded material on surplus models and ruin computations Discussions of nonparametric prediction intervals, option pricing diagnostics, variance of the loss function associated with standard actuarial models, and Gompertz and Makeham distributions Sections on the concept of actuarial statistics for a collection of stochastic status models The book presents a unified approach to both financial and actuarial modeling through the use of general status structures. The authors define future time-dependent financial actions in terms of a status structure that may be either deterministic or stochastic. They show how deterministic status structures lead to classical interest and annuity models, investment pricing models, and aggregate claim models. They also employ stochastic status structures to develop financial and actuarial models, such as surplus models, life insurance, and life annuity models.
Download or read book Modern Problems in Insurance Mathematics written by Dmitrii Silvestrov and published by Springer. This book was released on 2014-06-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of 21 papers presented at the International Cramér Symposium on Insurance Mathematics (ICSIM) held at Stockholm University in June, 2013. The book comprises selected contributions from several large research communities in modern insurance mathematics and its applications. The main topics represented in the book are modern risk theory and its applications, stochastic modelling of insurance business, new mathematical problems in life and non-life insurance and related topics in applied and financial mathematics. The book is an original and useful source of inspiration and essential reference for a broad spectrum of theoretical and applied researchers, research students and experts from the insurance business. In this way, Modern Problems in Insurance Mathematics will contribute to the development of research and academy–industry co-operation in the area of insurance mathematics and its applications.
Download or read book Handbook of Insurance written by Georges Dionne and published by Springer Science & Business Media. This book was released on 2013-12-02 with total page 1133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of the Handbook of Insurance reviews the last forty years of research developments in insurance and its related fields. A single reference source for professors, researchers, graduate students, regulators, consultants and practitioners, the book starts with the history and foundations of risk and insurance theory, followed by a review of prevention and precaution, asymmetric information, risk management, insurance pricing, new financial innovations, reinsurance, corporate governance, capital allocation, securitization, systemic risk, insurance regulation, the industrial organization of insurance markets and other insurance market applications. It ends with health insurance, longevity risk, long-term care insurance, life insurance financial products and social insurance. This second version of the Handbook contains 15 new chapters. Each of the 37 chapters has been written by leading authorities in risk and insurance research, all contributions have been peer reviewed, and each chapter can be read independently of the others.
Download or read book Stochastic Control in Insurance written by Hanspeter Schmidli and published by Springer Science & Business Media. This book was released on 2007-11-20 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Yet again, here is a Springer volume that offers readers something completely new. Until now, solved examples of the application of stochastic control to actuarial problems could only be found in journals. Not any more: this is the first book to systematically present these methods in one volume. The author starts with a short introduction to stochastic control techniques, then applies the principles to several problems. These examples show how verification theorems and existence theorems may be proved, and that the non-diffusion case is simpler than the diffusion case. Schmidli’s brilliant text also includes a number of appendices, a vital resource for those in both academic and professional settings.
Download or read book Asymptotology written by Igor V. Andrianov and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods belong to the, perhaps, most romantic area of modern mathematics. They are widely known and have been used in me chanics, physics and other exact sciences for many, many decades. But more than this, asymptotic ideas are found in all branches of human knowledge, indeed in all areas of life. In this broader context they have not and perhaps cannot be fully formalized. However, they are mar velous, they leave room for fantasy, guesses and intuition; they bring us very near to the border of the realm of art. Many books have been written and published about asymptotic meth ods. Most of them presume a mathematically sophisticated reader. The authors here attempt to describe asymptotic methods on a more accessi ble level, hoping to address a wider range of readers. They have avoided the extreme of banishing formulae entirely, as done in some popular science books that attempt to describe mathematical methods with no mathematics. This is impossible (and not wise). Rather, the authors have tried to keep the mathematics at a moderate level. At the same time, using simple examples, they think they have been able to illustrate all the key ideas of asymptotic methods and approaches, to depict in de tail the results of their application to various branches of knowledg- from astronomy, mechanics, and physics to biology, psychology and art. The book is supplemented by several appendices, one of which con tains the profound ideas of R. G.
Download or read book Introduction to Asymptotics written by Douglas Samuel Jones and published by World Scientific. This book was released on 1997 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A very attractive feature of the book is the numerous examples illustrating the methods. A fine collection of exercises enriches each chapter, challenging the reader to check his progress in understanding the methods".Mathematical Reviews"As an introductory book to asymptotics, with chapters on uniform asymptotics and exponential asymptotics, this book clearly fills a gap it has a friendly size and contains many convincing numerical examples and interesting exercises. Hence, I recommend the book to everyone who works in asymptotics".SIAM, 1998" it is an excellent book that contains interesting results and methods for the researchers. It will be useful for the students interested in analysis and lectures on asymptotic methods The reviewer recommends the book to everyone who is interested in analysis, engineers and specialists in ODE-s"Acta Sci. Math. (Szeged), 1999
Download or read book Granularity Theory with Applications to Finance and Insurance written by Patrick Gagliardini and published by Cambridge University Press. This book was released on 2014-10-06 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent financial crisis has heightened the need for appropriate methodologies for managing and monitoring complex risks in financial markets. The measurement, management, and regulation of risks in portfolios composed of credits, credit derivatives, or life insurance contracts is difficult because of the nonlinearities of risk models, dependencies between individual risks, and the several thousands of contracts in large portfolios. The granularity principle was introduced in the Basel regulations for credit risk to solve these difficulties in computing capital reserves. In this book, authors Patrick Gagliardini and Christian Gouriéroux provide the first comprehensive overview of the granularity theory and illustrate its usefulness for a variety of problems related to risk analysis, statistical estimation, and derivative pricing in finance and insurance. They show how the granularity principle leads to analytical formulas for risk analysis that are simple to implement and accurate even when the portfolio size is large.
Download or read book Stochastic Analysis with Financial Applications written by Arturo Kohatsu-Higa and published by Springer Science & Business Media. This book was released on 2011-07-22 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. The book also covers the areas of backward stochastic differential equations via the (non-linear) G-Brownian motion and the case of jump processes. Concerning the applications to finance, many of the articles deal with the valuation and hedging of credit risk in various forms, and include recent results on markets with transaction costs.
