{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T05:52:37Z","timestamp":1723182757304},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,11,9]],"date-time":"2014-11-09T00:00:00Z","timestamp":1415491200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2015,6]]},"DOI":"10.1007\/s10479-014-1748-6","type":"journal-article","created":{"date-parts":[[2014,11,14]],"date-time":"2014-11-14T18:09:50Z","timestamp":1415988590000},"page":"591-605","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Kusuoka representations of coherent risk measures in general probability spaces"],"prefix":"10.1007","volume":"229","author":[{"given":"Nilay","family":"Noyan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00e1bor","family":"Rudolf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,11,9]]},"reference":[{"issue":"3","key":"1748_CR1","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1111\/1467-9965.00068","volume":"9","author":"P Artzner","year":"1999","unstructured":"Artzner, P., Delbaen, F., Eber, J., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203\u2013228.","journal-title":"Mathematical Finance"},{"issue":"9","key":"1748_CR2","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1287\/mnsc.12.9.732","volume":"12","author":"M Bacharach","year":"1966","unstructured":"Bacharach, M. (1966). Matrix rounding problems. Management Science, 12(9), 732\u2013742.","journal-title":"Management Science"},{"issue":"6","key":"1748_CR3","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.1287\/opre.1080.0646","volume":"57","author":"D Bertsimas","year":"2009","unstructured":"Bertsimas, D., & Brown, D. B. (2009). Constructing uncertainty sets for robust linear optimization. Operations Research, 57(6), 1483\u20131495.","journal-title":"Operations Research"},{"issue":"1","key":"1748_CR4","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s11579-008-0013-7","volume":"2","author":"P Cheridito","year":"2008","unstructured":"Cheridito, P., & Li, T. (2008). Dual characterization of properties of risk measures on Orlicz hearts. Mathematics and Financial Economics, 2(1), 29\u201355.","journal-title":"Mathematics and Financial Economics"},{"issue":"4","key":"1748_CR5","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1111\/j.1467-9965.2005.00253.x","volume":"15","author":"R-A Dana","year":"2005","unstructured":"Dana, R.-A. (2005). A representation result for concave schur concave functions. Mathematical Finance, 15(4), 613\u2013634.","journal-title":"Mathematical Finance"},{"key":"1748_CR6","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s10479-010-0747-5","volume":"181","author":"D Dentcheva","year":"2010","unstructured":"Dentcheva, D., Penev, S., & Ruszczy\u0144ski, A. (2010). Kusuoka representation of higher order dual risk measures. Annals of Operations Research, 181, 325\u2013335.","journal-title":"Annals of Operations Research"},{"issue":"1","key":"1748_CR7","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1137\/120868311","volume":"23","author":"D Dentcheva","year":"2013","unstructured":"Dentcheva, D., & Ruszczy\u0144ski, A. (2013a). Common mathematical foundations of expected utility and dual utility theories. SIAM Journal on Optimization, 23(1), 381\u2013405.","journal-title":"SIAM Journal on Optimization"},{"key":"1748_CR8","doi-asserted-by":"crossref","unstructured":"Dentcheva, D., & Ruszczy\u0144ski, A. (2013b). Risk preferences on the space of quantile functions. Mathematical Programming, Ser: B (online first). doi: 10.1007\/s10107-013-0724-2 .","DOI":"10.1007\/s10107-013-0724-2"},{"key":"1748_CR9","doi-asserted-by":"crossref","unstructured":"F\u00f6llmer, H., & Schied, A. (2004). Stochastic finance. Number 27 in De Gruyter studies in mathematics. Berlin: de Gruyter, 2, rev. and extended edition.","DOI":"10.1515\/9783110212075"},{"key":"1748_CR10","doi-asserted-by":"crossref","unstructured":"Frittelli, M., & Rosazza Gianin, E. (2005). Law invariant convex risk measures. In Kusuoka, S., Maruyama, T. (Eds.), Advances in mathematical economics (Vo. 7, pp. 33\u201346).","DOI":"10.1007\/4-431-27233-X_2"},{"issue":"2","key":"1748_CR11","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1111\/j.1467-9965.2010.00464.x","volume":"22","author":"B Grechuk","year":"2012","unstructured":"Grechuk, B., & Zabarankin, M. (2012). Schur convex functionals: Fatou property and representation. Mathematical Finance, 22(2), 411\u2013418.","journal-title":"Mathematical Finance"},{"issue":"1","key":"1748_CR12","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/4-431-34342-3_4","volume":"9","author":"E Jouini","year":"2006","unstructured":"Jouini, E., Schachermayer, W., & Touzi, N. (2006). Law-invariant risk measures have the Fatou property. Advances in Mathematical Economics, 9(1), 49\u201371.","journal-title":"Advances in Mathematical Economics"},{"key":"1748_CR13","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/978-4-431-67891-5_4","volume":"3","author":"S Kusuoka","year":"2001","unstructured":"Kusuoka, S. (2001). On law invariant coherent risk measures. Advances in Mathematical Economics, 3, 83\u201395.","journal-title":"Advances in Mathematical Economics"},{"issue":"4","key":"1748_CR14","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1111\/j.1467-9965.2005.00255.x","volume":"15","author":"J Leitner","year":"2005","unstructured":"Leitner, J. (2005). A short note on second-order stochastic dominance preserving coherent risk measures. Mathematical Finance, 15(4), 649\u2013651.","journal-title":"Mathematical Finance"},{"key":"1748_CR15","volume-title":"Quantitative risk management: Concepts, techniques, and tools. Princeton series in finance","author":"A McNeil","year":"2005","unstructured":"McNeil, A., Frey, R., & Embrechts, P. (2005). Quantitative risk management: Concepts, techniques, and tools. Princeton series in finance. Princeton: Princeton University Press."},{"key":"1748_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3076-0","volume-title":"An introduction to copulas","author":"RB Nelsen","year":"1999","unstructured":"Nelsen, R. B. (1999). An introduction to copulas. New York: Springer."},{"key":"1748_CR17","unstructured":"Noyan, N., & Rudolf, G. (2012a). Kusuoka representations of coherent risk measures in finite probability spaces. Technical report, RUTCOR-Rutgers Center for Operations Research, RRR 33-2012. http:\/\/rutcor.rutgers.edu\/pub\/rrr\/reports2012\/33_2012.pdf ."},{"key":"1748_CR18","unstructured":"Noyan, N., & Rudolf, G. (2012b). Optimization with multivariate conditional value-at-risk-constraints. Technical report, Optimization online. http:\/\/www.optimization-online.org\/DB_FILE\/2012\/04\/3444.pdf ."},{"key":"1748_CR19","doi-asserted-by":"crossref","unstructured":"Noyan, N., & Rudolf, G. (2013). Optimization with multivariate conditional value-at-risk-constraints. Operations Research, 61(4), 990\u20131013.","DOI":"10.1287\/opre.2013.1186"},{"key":"1748_CR20","first-page":"377","volume-title":"Quantitative fund management, Chapman & Hall\/CRC financial mathematics series","author":"G Pflug","year":"2009","unstructured":"Pflug, G., & Wozabal, D. (2009). Ambiguity in portfolio selection. In A. H. Dempster, G. Pflug, & G. Mitra (Eds.), Quantitative fund management, Chapman & Hall\/CRC financial mathematics series (pp. 377\u2013391). Boca Raton, FL: CRC Press."},{"key":"1748_CR21","volume-title":"Probabilistic constrained optimization: Methodology and applications","author":"GC Pflug","year":"2000","unstructured":"Pflug, G. C. (2000). Some remarks on the value-at-risk and the conditional value-at-risk. In S. Uryasev (Ed.), Probabilistic constrained optimization: Methodology and applications. Dordrecht: Kluwer."},{"key":"1748_CR22","doi-asserted-by":"crossref","DOI":"10.1142\/6478","volume-title":"Modeling, managing and measuring risk","author":"GC Pflug","year":"2007","unstructured":"Pflug, G. C., & R\u00f6misch, W. (2007). Modeling, managing and measuring risk. Singapore: World Scientific publishing."},{"key":"1748_CR23","unstructured":"Pichler, A., & Shapiro, A. (2012). Uniqueness of Kusuoka representations. http:\/\/www.optimization-online.org\/DB_FILE\/2012\/10\/3660.pdf ."},{"key":"1748_CR24","doi-asserted-by":"crossref","unstructured":"Rockafellar, R. T. (2007). Coherent approaches to risk in optimization under uncertainty. Tutorials in operations research, 3, 38\u201361.","DOI":"10.1287\/educ.1073.0032"},{"issue":"3","key":"1748_CR25","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1287\/moor.1050.0186","volume":"31","author":"A Ruszczy\u0144ski","year":"2006","unstructured":"Ruszczy\u0144ski, A., & Shapiro, A. (2006). Optimization of convex risk functions. Mathematics of Operations Research, 31(3), 433\u2013452.","journal-title":"Mathematics of Operations Research"},{"key":"1748_CR26","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1287\/moor.1120.0563","volume":"38","author":"A Shapiro","year":"2013","unstructured":"Shapiro, A. (2013). On Kusuoka representation of law invariant risk measures. Mathematics of Operations Research, 38, 142\u2013152.","journal-title":"Mathematics of Operations Research"},{"key":"1748_CR27","doi-asserted-by":"crossref","unstructured":"Shapiro, A., Dentcheva, D., & Ruszczy\u0144ski, A. (2009). Lectures on stochastic programming: Modeling and theory. Philadelphia, USA: The society for industrial and applied mathematics and the mathematical programming society.","DOI":"10.1137\/1.9780898718751"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-014-1748-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-014-1748-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-014-1748-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T14:09:54Z","timestamp":1559138994000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-014-1748-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,9]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,6]]}},"alternative-id":["1748"],"URL":"https:\/\/doi.org\/10.1007\/s10479-014-1748-6","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,9]]}}}