On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation
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Published version
Accepted version
Author(s)
Madan, D
Pistorius, MR
Stadje, M
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.
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.
Date Issued
2017-08-16
Date Acceptance
2017-03-20
Citation
Finance and Stochastics, 2017, 21 (4), pp.10736-1102
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.
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.
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Subjects
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