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

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1301.3531SUB.pdfAccepted version488.1 kBAdobe PDFView/Open
10.1007%2Fs00780-017-0339-1.pdfPublished version956.3 kBAdobe PDFView/Open
Title: On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation
Authors: Madan, D
Pistorius, MR
Stadje, M
Item Type: Journal Article
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 time- and spatial-mesh sizes. To illustrate its use in financial optimisation problems, we analyse a dynamic portfolio optimisation problem under a DSR.
Issue Date: 16-Aug-2017
Date of Acceptance: 20-Mar-2017
URI: http://hdl.handle.net/10044/1/47931
DOI: https://dx.doi.org/10.1007/s00780-017-0339-1
ISSN: 1432-1122
Publisher: Springer Verlag (Germany)
Start Page: 10736
End Page: 1102
Journal / Book Title: Finance and Stochastics
Volume: 21
Issue: 4
Copyright Statement: © The Author(s) 2017 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: Social Sciences
Science & Technology
Physical Sciences
Business, Finance
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Statistics & Probability
Business & Economics
Mathematics
Mathematical Methods In Social Sciences
Spectral risk measure
Dynamic risk measure
g-expectation
Choquet expectation
Distortion
(Strong) Time-consistency
Limit theorem
Dynamic portfolio optimisation
STOCHASTIC DIFFERENCE-EQUATIONS
NONLINEAR EXPECTATIONS
CONTINUOUS-TIME
DISCRETE-TIME
ASSET RETURNS
COHERENT RISK
UTILITY
CONSISTENCY
JUMPS
CONVERGENCE
0102 Applied Mathematics
0104 Statistics
Finance
Publication Status: Published
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences



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