Ambit Stochastics

by Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart

Overview

Drawing on advanced probability theory, Ambit Shastics is used to model shastic processes which depend on both time and space. This monograph, the first on the subject, provides a reference for this burgeoning field, complete with the applications that have driven its development.

Unique to Ambit Shastics are ambit sets, which allow the delimitation of space-time to a zone of interest, and ambit fields, which are particularly well-adapted to modelling shastic volatility or intermittency. These attributes lend themselves notably to applications in the statistical theory of turbulence and financial econometrics. In addition to the theory and applications of Ambit Shastics, the book also contains new theory on the simulation of ambit fields and a comprehensive shastic integration theory for Volterra processes in a non-semimartingale context.

Written by pioneers in the subject, this book will appeal to researchers and graduate students interested in empirical shastic modelling.

Product Details

ISBN-13:	9783030068028
Publisher:	Springer International Publishing
Publication date:	12/19/2018
Series:	Probability Theory and Stochastic Modelling , #88
Edition description:	Softcover reprint of the original 1st ed. 2018
Pages:	402
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Ole Barndorff-Nielsen is well known for his manifold contributions to the theory and applications of probability and mathematical statistics, as described in the introductions of The Fascination of Probability, Statistics and Their Applications, Springer 2016. He has contributed to various fields, including statistical inference, sedimentology, infinite divisibility and Levy theory, homogeneous turbulence, and financial econometrics. Together with Jürgen Schmiegel he has founded the field of ambit shastics.

Fred Espen Benth’s research focuses on shastic analysis and its applications to energy and finance. He has contributed to risk management analysis of financial markets for weather and energy, as well as theoretical developments of shastic calculus, including non-semimartingale shastic integration. Recently he has developed shastic volatility models and autoregressive processes in the infinite dimensional context.

Almut E. D. Veraart is a statistician and probabilist with an interest in developing shastic models and statistical methods for finance, energy markets and weather and environmental variables. Her main methodological contributions are in statistical finance focusing on shastic volatility modelling and estimation based on high-frequency data and in spatio-temporal statistics dealing with simulation and inference for ambit fields.

Table of Contents

Part I The purely temporal case.- 1 Volatility modulated Volterra processes.- 2 Simulation.- 3 Asymptotic theory for power variation of LSS processes.- 4 Integration with respect to volatility modulated Volterra processes.- Part II The spatio-temporal case.- 5 The ambit framework.- 6 Representation and simulation of ambit fields.- 7 Shastic integration with ambit fields as integrators.- 8 Trawl processes.- Part III Applications.- 9 Turbulence modelling.- 10 Shastic modelling of energy spot prices by LSS processes.- 11 Forward curve modelling by ambit fields.- Appendix A: Bessel functions.- Appendix B: Generalised hyperbolic distribution.- References.- Index.

Editorial Reviews

The author pays a great attention to diverse methods of numerical integration and simulation algorithms. … The authors have written a fundamental book on contemporary probability theory and its applications. The book can be strongly recommended to theorists and applied scientists.” (Jordan M. Stoyanov, zbMATH 1472.60002, 2021)”

“The book is very well written … . this monograph is particularly suitable for getting acquainted with the subject, or for getting precise material on one particular sub-topic about ambit fields.” (Anthony Réveillac, Mathematical Reviews, January, 2020)

From the Publisher