From Independence to Dependence via Copulas and U-statistics

Rustam Ibragimov and Artem Prokhorov

Chapter 3 in Heavy Tails and Copulas:Topics in Dependence Modelling in Economics and Finance, 2017, pp 47-111 from World Scientific Publishing Co. Pte. Ltd.

Abstract: In this chapter, we show how to go from independent risks to risks with an arbitrary dependence structure. In other words, we represent any joint distribution and any copula function using certain functions of independent random variables known as U-statistics. We also discuss various dependence measures that are useful in this context, including a new measure suitable for measuring dependence between vectors rather than between scalars. An interesting application of this chapter’s theory is to pricing options.

Keywords: Heavy-Tailed Distribution; Copulas; Tail Dependence; Majorization Theory; Financial Contagion; Crises (search for similar items in EconPapers)
Date: 2017
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