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Stochastic Processes with Jumps

In: HANDBOOK OF HEAVY-TAILED DISTRIBUTIONS IN ASSET MANAGEMENT AND RISK MANAGEMENT

Author

Listed:
  • Michele Leonardo Bianchi
  • Stoyan V Stoyanov
  • Gian Luca Tassinari
  • Frank J Fabozzi
  • Sergio M Focardi

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.

Suggested Citation

  • Michele Leonardo Bianchi & Stoyan V Stoyanov & Gian Luca Tassinari & Frank J Fabozzi & Sergio M Focardi, 2019. "Stochastic Processes with Jumps," World Scientific Book Chapters, in: HANDBOOK OF HEAVY-TAILED DISTRIBUTIONS IN ASSET MANAGEMENT AND RISK MANAGEMENT, chapter 3, pages 71-106, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789813276208_0003
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    More about this item

    Keywords

    Heavy Tail Distributions; Fat Tail Distributions; Lévy Processes; Tempered Stable Distributions; Multivariate Time-changed Brownian Motion; Extreme Value Theory; Risk Management;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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