A Levy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. The need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Levy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Levy processes and their enormous flexibility in modeling tails, dependence and path behavior.
This volume, with an excellent...
A Levy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. The need f...
Both in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations in financial data, stock market shocks, risk management, ...) play an increasingly important role. This book sets out to bridge the gap between the existing theory and practical applications both from a probabilistic as well as from a statistical point of view. Whatever new theory is presented is always motivated by relevant real-life examples. The numerous illustrations and examples, and the extensive bibliography make this book an ideal reference text for...
Both in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations in financial da...
Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory.
This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can...
Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, b...
The second edition of this book contains both basic and more advanced - terial on non-life insurance mathematics. Parts I and II of the book cover the basic course of the ?rst edition; this text has changed very little. It aims at the undergraduate (bachelor) actuarial student as a ?rst introduction to the topics of non-life insurance mathematics. Parts III and IV are new. They can serve as an independent course on stochastic models of non-life insurance mathematics at the graduate (master) level. The basic themes in all parts of this book are point process theory, the Poisson and compound...
The second edition of this book contains both basic and more advanced - terial on non-life insurance mathematics. Parts I and II of the book cover the...
"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
"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...
This book contains accessible surveys by several leading experts in the field. The first part is a thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data, starting from the classical contributions of Billingsley and including present day research. The bibliography provides an excellent basis for further studies. The remaining parts of the book give an overview of the most recent applications in various fields related to empirical processes such as spectral analysis of time series, the bootstrap for stationary sequences, extreme value...
This book contains accessible surveys by several leading experts in the field. The first part is a thorough and comprehensive introduction to the exis...
A Levy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Levy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Levy processes. Researchers and practitioners...
A Levy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingale...
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t, B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes,...
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study ...
