Central limit theorems for law-invariant coherent risk measures - Denis Belomestny; Volker Krätschmer (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2010)
In this paper we study the asymptotic properties of the canonical plug-in estimates for law-invariant coherent risk measures. Under rather mild conditions not relying on the explicit representation of the risk measure under consideration, we first prove a central limit theorem for independent identically distributed data and then extend it to the case of weakly dependent ones. Finally, a number of illustrating examples is presented.
Keywords: D81; G32; 330; law-invariant coherent risk measures; canonical plug-in estimates; functional central limit theorems; weak dependence; Risikomanagement; Theorie