Stochastic Processes with Jumps

Michele Leonardo Bianchi, Stoyan V Stoyanov, Gian Luca Tassinari, Frank Fabozzi () and Sergio M Focardi

Chapter 3 in Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management, 2019, pp 71-106 from World Scientific Publishing Co. Pte. Ltd.

Abstract: In this chapter, we summarize the main results for Lévy processes. We focus our attention on definitions and properties that we will need in the chapters that follow in this book. The main topics covered in this chapter are:basic definitions of stochastic processes;the definition of Lévy processes;some basic results for Lévy processes;the modeling of asset log-prices with Lévy processes;a discussion about the change of measure for Lévy processes.

Keywords: Heavy Tail Distributions; Fat Tail Distributions; Lévy Processes; Tempered Stable Distributions; Multivariate Time-changed Brownian Motion; Extreme Value Theory; Risk Management (search for similar items in EconPapers)
JEL-codes: C02 G32 (search for similar items in EconPapers)
Date: 2019
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