A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle

A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for d assets with transaction costs or illiquidity and possible trading constraints are considered on a finite probability space. The set of capital requirements at each t...

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Veröffentlicht in:Journal of global optimization Jg. 68; H. 1; S. 47 - 69
Hauptverfasser: Feinstein, Zachary, Rudloff, Birgit
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.05.2017
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Computer Science
Constraint modelling
Dynamic programming
Markets
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Multivariate analysis
Operations Research/Decision Theory
Optimization
Optimization techniques
Random variables
Real Functions
Risk
Risk assessment
Studies
Time measurement
Bellman’s principle
Dynamic risk measures
90C39
Dynamic programming
Set-valued risk measures
Transaction costs
91B30
46N10
Vector optimization
26E25
ISSN:0925-5001, 1573-2916
Online-Zugang:Volltext
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Zusammenfassung:A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for d assets with transaction costs or illiquidity and possible trading constraints are considered on a finite probability space. The set of capital requirements at each time and state is calculated recursively backwards in time along the event tree. We motivate why the proposed procedure can be seen as a set-valued Bellman’s principle, that might be of independent interest within the growing field of set optimization. We give conditions under which the backwards calculation of the sets reduces to solving a sequence of linear, respectively convex vector optimization problems. Numerical examples are given and include superhedging under illiquidity, the set-valued entropic risk measure, and the multi-portfolio time consistent version of the relaxed worst case risk measure and of the set-valued average value at risk.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-016-0459-8