Multivariate Time-Changed Brownian Motion

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

Chapter 7 in Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management, 2019, pp 277-321 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The main topics covered in this chapter are:the history of time-changed Brownian motion and why this process has been applied to finance;the main properties and formulas for different parametric examples of multivariate time-changed Brownian motion;the relation between multivariate time-changed Brownian motion and multivariate normal mean–variance mixture distributions;the derivation of the closed formula for the density function of some multivariate normal mean–variance mixture laws;the evaluation of the probability density function of a multivariate normal mean–variance mixture law when only the characteristic function of the mixing distribution is available in closed form while the density function is not;how to generate sample draws from a multivariate normal mean–variance mixture law.

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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