Bücher der Reihe Advanced Series on Statistical Science & Applied Probability

Provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law. This book is suitable for graduate-level courses and students, as well as for researchers and practitioners in financial mathematics and econometrics.

Offers a treatment on the stochastic modeling of energy markets. This book describes Ornstein-Uhlenbeck processes as the basic modeling tool for spot price dynamics, where innovations are driven by time-inhomogeneous jump processes.

This text provides information for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty. It introduces the reader to the main concepts, notions and results of stochastic financial mathematics.

Provides a tool for weather risk management and the markets for these exotic financial products are gradually emerging in size and importance. This title presents an analysis of such weather derivatives, including financial contracts on temperature, wind and rain.

Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.

An elementary introduction to modelling with Ito integral or stochastic differential equations, 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.

Valuation and hedging of financial derivatives are intrinsically linked concepts. Choosing appropriate hedging techniques depends on both the type of derivative and assumptions placed on the underlying stochastic process. This title provides a systematic treatment of hedging in incomplete markets.

This unique volume discusses some recent developments in the theory of spatial branching processes and superprocesses, with special emphasis on spines, Laws of Large Numbers, interactions and random media.Although this book is mainly written for mathematicians, the models discussed are relevant to certain models in population biology, and are thus hopefully interesting to the applied mathematician/biologist as well.The necessary background material in probability and analysis is provided in a comprehensive introductory chapter. Historical notes and several exercises are provided to complement each chapter.

In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term "neo-Fisherian" highlights this.

Offers a comprehensive treatment of the classical and modern ruin probability theory. This title includes topics such as: Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations, finite horizon ruin probabilities, and extensions of the classical compound Poisson model to allow for reserve-dependent premiums.

This book introduces the mathematics of stochastic interest rate modeling and the pricing of related derivatives, based on a step-by-step presentation of concepts with a focus on explicit calculations.