On Dynamic Spectral Risk Measures and a Limit Theorem

53 Pages Posted: 26 Jul 2015

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Martijn Pistorius

Imperial College London

Mitja Stadje

Tilburg University - Department of Econometrics & Operations Research

Date Written: July 24, 2015

Abstract

In this paper we explore a novel way to combine the dynamic notion of time-consistency with the static notion of quantile-based coherent risk-measure or spectral risk measure, of which Expected Shortfall is a prime example. We introduce a class of dynamic risk measures in terms of a certain family of g-expectations driven by Wiener and Poisson point processes. In analogy with the static case, we show that these risk measures, which we label dynamic spectral risk measures, are locally law-invariant and additive on the set of pathwise increasing random variables. We substantiate the link between dynamic spectral risk measures and their static counterparts by establishing a limit theorem for general path-functionals which shows that such dynamic risk measures arise as limits under vanishing time-step of iterated spectral risk measures driven by approximating lattice random walks. This involves a certain non-standard scaling of the corresponding spectral weight-measures that we identify explicitly.

Suggested Citation

Madan, Dilip B. and Pistorius, Martijn and Stadje, Mitja, On Dynamic Spectral Risk Measures and a Limit Theorem (July 24, 2015). Robert H. Smith School Research Paper No. RHS 2635636, Available at SSRN: https://ssrn.com/abstract=2635636 or http://dx.doi.org/10.2139/ssrn.2635636

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

Martijn Pistorius

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/people/m.pistorius

Mitja Stadje

Tilburg University - Department of Econometrics & Operations Research ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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