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
Autor*in: |
Feinstein, Zachary [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
2016 |
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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 |
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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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OLC203064966X |
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10.1007/s10898-016-0459-8 doi (DE-627)OLC203064966X (DE-He213)s10898-016-0459-8-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 83.00 bkl Feinstein, Zachary verfasserin (orcid)0000-0002-6733-5724 aut A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 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. Dynamic risk measures Transaction costs Set-valued risk measures Vector optimization Dynamic programming Bellman’s principle Rudloff, Birgit (orcid)0000-0003-1675-5451 aut Enthalten in Journal of global optimization Springer US, 1991 68(2016), 1 vom: 31. Aug., Seite 47-69 (DE-627)130979074 (DE-600)1074566-X (DE-576)034188533 0925-5001 nnns volume:68 year:2016 number:1 day:31 month:08 pages:47-69 https://doi.org/10.1007/s10898-016-0459-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4266 GBV_ILN_4311 83.00 VZ AR 68 2016 1 31 08 47-69 |
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10.1007/s10898-016-0459-8 doi (DE-627)OLC203064966X (DE-He213)s10898-016-0459-8-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 83.00 bkl Feinstein, Zachary verfasserin (orcid)0000-0002-6733-5724 aut A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 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. Dynamic risk measures Transaction costs Set-valued risk measures Vector optimization Dynamic programming Bellman’s principle Rudloff, Birgit (orcid)0000-0003-1675-5451 aut Enthalten in Journal of global optimization Springer US, 1991 68(2016), 1 vom: 31. Aug., Seite 47-69 (DE-627)130979074 (DE-600)1074566-X (DE-576)034188533 0925-5001 nnns volume:68 year:2016 number:1 day:31 month:08 pages:47-69 https://doi.org/10.1007/s10898-016-0459-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4266 GBV_ILN_4311 83.00 VZ AR 68 2016 1 31 08 47-69 |
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10.1007/s10898-016-0459-8 doi (DE-627)OLC203064966X (DE-He213)s10898-016-0459-8-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 83.00 bkl Feinstein, Zachary verfasserin (orcid)0000-0002-6733-5724 aut A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 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. Dynamic risk measures Transaction costs Set-valued risk measures Vector optimization Dynamic programming Bellman’s principle Rudloff, Birgit (orcid)0000-0003-1675-5451 aut Enthalten in Journal of global optimization Springer US, 1991 68(2016), 1 vom: 31. Aug., Seite 47-69 (DE-627)130979074 (DE-600)1074566-X (DE-576)034188533 0925-5001 nnns volume:68 year:2016 number:1 day:31 month:08 pages:47-69 https://doi.org/10.1007/s10898-016-0459-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4266 GBV_ILN_4311 83.00 VZ AR 68 2016 1 31 08 47-69 |
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10.1007/s10898-016-0459-8 doi (DE-627)OLC203064966X (DE-He213)s10898-016-0459-8-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 83.00 bkl Feinstein, Zachary verfasserin (orcid)0000-0002-6733-5724 aut A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 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. Dynamic risk measures Transaction costs Set-valued risk measures Vector optimization Dynamic programming Bellman’s principle Rudloff, Birgit (orcid)0000-0003-1675-5451 aut Enthalten in Journal of global optimization Springer US, 1991 68(2016), 1 vom: 31. Aug., Seite 47-69 (DE-627)130979074 (DE-600)1074566-X (DE-576)034188533 0925-5001 nnns volume:68 year:2016 number:1 day:31 month:08 pages:47-69 https://doi.org/10.1007/s10898-016-0459-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4266 GBV_ILN_4311 83.00 VZ AR 68 2016 1 31 08 47-69 |
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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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container_issue |
1 |
title_short |
A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle |
url |
https://doi.org/10.1007/s10898-016-0459-8 |
remote_bool |
false |
author2 |
Rudloff, Birgit |
author2Str |
Rudloff, Birgit |
ppnlink |
130979074 |
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hochschulschrift_bool |
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doi_str |
10.1007/s10898-016-0459-8 |
up_date |
2024-07-04T02:44:13.016Z |
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