Time consistency for set-valued dynamic risk measures for bounded discrete-time processes
Abstract In this paper, we introduce two kinds of time consistent properties for set-valued dynamic risk measures for discrete-time processes that are adapted to a given filtration, named time consistency and multi-portfolio time consistency. Equivalent characterizations of multi-portfolio time cons...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chen, Yanhong [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag GmbH Germany, part of Springer Nature 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Mathematics and financial economics - Berlin : Springer, 2007, 12(2017), 3 vom: 30. Nov., Seite 305-333 |
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| Übergeordnetes Werk: |
volume:12 ; year:2017 ; number:3 ; day:30 ; month:11 ; pages:305-333 |
| Links: |
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| DOI / URN: |
10.1007/s11579-017-0205-0 |
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| Katalog-ID: |
SPR020842090 |
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| 520 | |a Abstract In this paper, we introduce two kinds of time consistent properties for set-valued dynamic risk measures for discrete-time processes that are adapted to a given filtration, named time consistency and multi-portfolio time consistency. Equivalent characterizations of multi-portfolio time consistency are deduced for normalized dynamic risk measures. In the normalized case, multi-portfolio time consistency is equivalent to the recursive form for risk measures as well as a decomposition property for the acceptance sets. The relations between time consistency and multi-portfolio time consistency are addressed. We also provide a way to construct multi-portfolio time consistent versions of any dynamic risk measure. Finally, we investigate the relationship about time consistency and multi-portfolio time consistency between risk measures for processes and risk measures for random vectors on some product space. | ||
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| 650 | 4 | |a Time consistency |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Multi-portfolio time consistency |7 (dpeaa)DE-He213 | |
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10.1007/s11579-017-0205-0 doi (DE-627)SPR020842090 (SPR)s11579-017-0205-0-e DE-627 ger DE-627 rakwb eng Chen, Yanhong verfasserin aut Time consistency for set-valued dynamic risk measures for bounded discrete-time processes 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2017 Abstract In this paper, we introduce two kinds of time consistent properties for set-valued dynamic risk measures for discrete-time processes that are adapted to a given filtration, named time consistency and multi-portfolio time consistency. Equivalent characterizations of multi-portfolio time consistency are deduced for normalized dynamic risk measures. In the normalized case, multi-portfolio time consistency is equivalent to the recursive form for risk measures as well as a decomposition property for the acceptance sets. The relations between time consistency and multi-portfolio time consistency are addressed. We also provide a way to construct multi-portfolio time consistent versions of any dynamic risk measure. Finally, we investigate the relationship about time consistency and multi-portfolio time consistency between risk measures for processes and risk measures for random vectors on some product space. Dynamic risk measures (dpeaa)DE-He213 Set-valued risk measures (dpeaa)DE-He213 Bounded discrete-time processes (dpeaa)DE-He213 Time consistency (dpeaa)DE-He213 Multi-portfolio time consistency (dpeaa)DE-He213 Hu, Yijun aut Enthalten in Mathematics and financial economics Berlin : Springer, 2007 12(2017), 3 vom: 30. Nov., Seite 305-333 (DE-627)546005721 (DE-600)2389109-9 1862-9660 nnns volume:12 year:2017 number:3 day:30 month:11 pages:305-333 https://dx.doi.org/10.1007/s11579-017-0205-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2017 3 30 11 305-333 |
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10.1007/s11579-017-0205-0 doi (DE-627)SPR020842090 (SPR)s11579-017-0205-0-e DE-627 ger DE-627 rakwb eng Chen, Yanhong verfasserin aut Time consistency for set-valued dynamic risk measures for bounded discrete-time processes 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2017 Abstract In this paper, we introduce two kinds of time consistent properties for set-valued dynamic risk measures for discrete-time processes that are adapted to a given filtration, named time consistency and multi-portfolio time consistency. Equivalent characterizations of multi-portfolio time consistency are deduced for normalized dynamic risk measures. In the normalized case, multi-portfolio time consistency is equivalent to the recursive form for risk measures as well as a decomposition property for the acceptance sets. The relations between time consistency and multi-portfolio time consistency are addressed. We also provide a way to construct multi-portfolio time consistent versions of any dynamic risk measure. Finally, we investigate the relationship about time consistency and multi-portfolio time consistency between risk measures for processes and risk measures for random vectors on some product space. Dynamic risk measures (dpeaa)DE-He213 Set-valued risk measures (dpeaa)DE-He213 Bounded discrete-time processes (dpeaa)DE-He213 Time consistency (dpeaa)DE-He213 Multi-portfolio time consistency (dpeaa)DE-He213 Hu, Yijun aut Enthalten in Mathematics and financial economics Berlin : Springer, 2007 12(2017), 3 vom: 30. Nov., Seite 305-333 (DE-627)546005721 (DE-600)2389109-9 1862-9660 nnns volume:12 year:2017 number:3 day:30 month:11 pages:305-333 https://dx.doi.org/10.1007/s11579-017-0205-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2017 3 30 11 305-333 |
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10.1007/s11579-017-0205-0 doi (DE-627)SPR020842090 (SPR)s11579-017-0205-0-e DE-627 ger DE-627 rakwb eng Chen, Yanhong verfasserin aut Time consistency for set-valued dynamic risk measures for bounded discrete-time processes 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2017 Abstract In this paper, we introduce two kinds of time consistent properties for set-valued dynamic risk measures for discrete-time processes that are adapted to a given filtration, named time consistency and multi-portfolio time consistency. Equivalent characterizations of multi-portfolio time consistency are deduced for normalized dynamic risk measures. In the normalized case, multi-portfolio time consistency is equivalent to the recursive form for risk measures as well as a decomposition property for the acceptance sets. The relations between time consistency and multi-portfolio time consistency are addressed. We also provide a way to construct multi-portfolio time consistent versions of any dynamic risk measure. Finally, we investigate the relationship about time consistency and multi-portfolio time consistency between risk measures for processes and risk measures for random vectors on some product space. Dynamic risk measures (dpeaa)DE-He213 Set-valued risk measures (dpeaa)DE-He213 Bounded discrete-time processes (dpeaa)DE-He213 Time consistency (dpeaa)DE-He213 Multi-portfolio time consistency (dpeaa)DE-He213 Hu, Yijun aut Enthalten in Mathematics and financial economics Berlin : Springer, 2007 12(2017), 3 vom: 30. Nov., Seite 305-333 (DE-627)546005721 (DE-600)2389109-9 1862-9660 nnns volume:12 year:2017 number:3 day:30 month:11 pages:305-333 https://dx.doi.org/10.1007/s11579-017-0205-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2017 3 30 11 305-333 |
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10.1007/s11579-017-0205-0 doi (DE-627)SPR020842090 (SPR)s11579-017-0205-0-e DE-627 ger DE-627 rakwb eng Chen, Yanhong verfasserin aut Time consistency for set-valued dynamic risk measures for bounded discrete-time processes 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2017 Abstract In this paper, we introduce two kinds of time consistent properties for set-valued dynamic risk measures for discrete-time processes that are adapted to a given filtration, named time consistency and multi-portfolio time consistency. Equivalent characterizations of multi-portfolio time consistency are deduced for normalized dynamic risk measures. In the normalized case, multi-portfolio time consistency is equivalent to the recursive form for risk measures as well as a decomposition property for the acceptance sets. The relations between time consistency and multi-portfolio time consistency are addressed. We also provide a way to construct multi-portfolio time consistent versions of any dynamic risk measure. Finally, we investigate the relationship about time consistency and multi-portfolio time consistency between risk measures for processes and risk measures for random vectors on some product space. Dynamic risk measures (dpeaa)DE-He213 Set-valued risk measures (dpeaa)DE-He213 Bounded discrete-time processes (dpeaa)DE-He213 Time consistency (dpeaa)DE-He213 Multi-portfolio time consistency (dpeaa)DE-He213 Hu, Yijun aut Enthalten in Mathematics and financial economics Berlin : Springer, 2007 12(2017), 3 vom: 30. Nov., Seite 305-333 (DE-627)546005721 (DE-600)2389109-9 1862-9660 nnns volume:12 year:2017 number:3 day:30 month:11 pages:305-333 https://dx.doi.org/10.1007/s11579-017-0205-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2017 3 30 11 305-333 |
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Enthalten in Mathematics and financial economics 12(2017), 3 vom: 30. Nov., Seite 305-333 volume:12 year:2017 number:3 day:30 month:11 pages:305-333 |
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Enthalten in Mathematics and financial economics 12(2017), 3 vom: 30. Nov., Seite 305-333 volume:12 year:2017 number:3 day:30 month:11 pages:305-333 |
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Chen, Yanhong |
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Time consistency for set-valued dynamic risk measures for bounded discrete-time processes Dynamic risk measures (dpeaa)DE-He213 Set-valued risk measures (dpeaa)DE-He213 Bounded discrete-time processes (dpeaa)DE-He213 Time consistency (dpeaa)DE-He213 Multi-portfolio time consistency (dpeaa)DE-He213 |
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time consistency for set-valued dynamic risk measures for bounded discrete-time processes |
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Time consistency for set-valued dynamic risk measures for bounded discrete-time processes |
| abstract |
Abstract In this paper, we introduce two kinds of time consistent properties for set-valued dynamic risk measures for discrete-time processes that are adapted to a given filtration, named time consistency and multi-portfolio time consistency. Equivalent characterizations of multi-portfolio time consistency are deduced for normalized dynamic risk measures. In the normalized case, multi-portfolio time consistency is equivalent to the recursive form for risk measures as well as a decomposition property for the acceptance sets. The relations between time consistency and multi-portfolio time consistency are addressed. We also provide a way to construct multi-portfolio time consistent versions of any dynamic risk measure. Finally, we investigate the relationship about time consistency and multi-portfolio time consistency between risk measures for processes and risk measures for random vectors on some product space. © Springer-Verlag GmbH Germany, part of Springer Nature 2017 |
| abstractGer |
Abstract In this paper, we introduce two kinds of time consistent properties for set-valued dynamic risk measures for discrete-time processes that are adapted to a given filtration, named time consistency and multi-portfolio time consistency. Equivalent characterizations of multi-portfolio time consistency are deduced for normalized dynamic risk measures. In the normalized case, multi-portfolio time consistency is equivalent to the recursive form for risk measures as well as a decomposition property for the acceptance sets. The relations between time consistency and multi-portfolio time consistency are addressed. We also provide a way to construct multi-portfolio time consistent versions of any dynamic risk measure. Finally, we investigate the relationship about time consistency and multi-portfolio time consistency between risk measures for processes and risk measures for random vectors on some product space. © Springer-Verlag GmbH Germany, part of Springer Nature 2017 |
| abstract_unstemmed |
Abstract In this paper, we introduce two kinds of time consistent properties for set-valued dynamic risk measures for discrete-time processes that are adapted to a given filtration, named time consistency and multi-portfolio time consistency. Equivalent characterizations of multi-portfolio time consistency are deduced for normalized dynamic risk measures. In the normalized case, multi-portfolio time consistency is equivalent to the recursive form for risk measures as well as a decomposition property for the acceptance sets. The relations between time consistency and multi-portfolio time consistency are addressed. We also provide a way to construct multi-portfolio time consistent versions of any dynamic risk measure. Finally, we investigate the relationship about time consistency and multi-portfolio time consistency between risk measures for processes and risk measures for random vectors on some product space. © Springer-Verlag GmbH Germany, part of Springer Nature 2017 |
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Time consistency for set-valued dynamic risk measures for bounded discrete-time processes |
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https://dx.doi.org/10.1007/s11579-017-0205-0 |
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Hu, Yijun |
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10.1007/s11579-017-0205-0 |
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