WIAS Preprint No. 1551, (2010)

Central limit theorems for law-invariant coherent risk measures


  • Belomestny, Denis
  • Krätschmer, Volker

2010 Mathematics Subject Classification

  • 60F05 60F12 62F17


  • law-invariant coherent risk measures, canonical plug-in estimates, functional central limit theorems, weak dependence


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.

Appeared in

  • J. Appl. Probab., 49 (2012) pp. 1--21.

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