A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle
Abstract 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...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Feinstein, Zachary [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of global optimization - Springer US, 1991, 68(2016), 1 vom: 31. Aug., Seite 47-69 |
|---|---|
| Übergeordnetes Werk: |
volume:68 ; year:2016 ; number:1 ; day:31 ; month:08 ; pages:47-69 |
| Links: |
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| DOI / URN: |
10.1007/s10898-016-0459-8 |
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| 520 | |a Abstract 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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| title_sort |
a recursive algorithm for multivariate risk measures and a set-valued bellman’s principle |
| title_auth |
A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle |
| abstract |
Abstract 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. © Springer Science+Business Media New York 2016 |
| abstractGer |
Abstract 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. © Springer Science+Business Media New York 2016 |
| abstract_unstemmed |
Abstract 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. © Springer Science+Business Media New York 2016 |
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| title_short |
A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle |
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https://doi.org/10.1007/s10898-016-0459-8 |
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Rudloff, Birgit |
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Rudloff, Birgit |
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10.1007/s10898-016-0459-8 |
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2024-07-04T02:44:13.016Z |
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