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Asymptotic consistency of risk functionals. (English) Zbl 1175.62113

Summary: Risk measures are functionals on spaces of random variables designed to quantify financial risks. We consider the statistical properties of plug-in estimates for the broad class of coherent, law invariant risk functionals. In particular, we provide several sets of sufficient conditions to establish asymptotic consistency based on a general representation result for this class of functionals. We demonstrate the applicability of our approach by applying it to several well-known examples of risk functionals.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
46N30 Applications of functional analysis in probability theory and statistics
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