On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation

D. Madan (), M. Pistorius () and M. Stadje ()
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D. Madan: University of Maryland
M. Pistorius: Imperial College London
M. Stadje: Universität Ulm

Finance and Stochastics, 2017, vol. 21, issue 4, No 6, 1073-1102

Abstract: Abstract In this paper, we propose the notion of continuous-time dynamic spectral risk measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may be considered to be (strongly) time-consistent continuous-time extensions of iterated spectral risk measures, which are obtained by iterating a given spectral risk measure (such as expected shortfall) along a given time-grid. Specifically, we demonstrate that any DSR arises in the limit of a sequence of such iterated spectral risk measures driven by lattice random walks, under suitable scaling and vanishing temporal and spatial mesh sizes. To illustrate its use in financial optimisation problems, we analyse a dynamic portfolio optimisation problem under a DSR.

Keywords: Spectral risk measure; Dynamic risk measure; g $g$ -expectation; Choquet expectation; Distortion; (Strong) Time-consistency; Limit theorem; Dynamic portfolio optimisation; 60H10; 91B30 (search for similar items in EconPapers)
JEL-codes: G32 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s00780-017-0339-1

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