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Random Variables

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

After formally introducing the notion of random variable and some related concepts, in this chapter we look at discrete and absolutely continuous random variables. We focus our attention on definitions and properties that will be needed in the chapters that follow. The main topics covered in this chapter are:basic definitions of probability theory;the definition of the characteristic function and other generating functions, and their main properties for real-valued random variables;a review of some univariate discrete random variables (Bernoulli, binomial and Poisson);a review of some univariate continuous random variables (gamma, exponential, inverse Gaussian, normal, log-normal, variance gamma, normal inverse Gaussian);a review of the multivariate normal distribution.

Suggested Citation

  • Michele Leonardo Bianchi & Stoyan V Stoyanov & Gian Luca Tassinari & Frank J Fabozzi & Sergio M Focardi, 2019. "Random Variables," World Scientific Book Chapters,in: HANDBOOK OF HEAVY-TAILED DISTRIBUTIONS IN ASSET MANAGEMENT AND RISK MANAGEMENT, chapter 2, pages 23-70 World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789813276208_0002
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    Keywords

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

    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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