{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T01:55:33Z","timestamp":1776822933683,"version":"3.51.2"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,7,4]],"date-time":"2009-07-04T00:00:00Z","timestamp":1246665600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2010,4]]},"DOI":"10.1007\/s10479-009-0586-4","type":"journal-article","created":{"date-parts":[[2009,7,3]],"date-time":"2009-07-03T10:24:59Z","timestamp":1246616699000},"page":"221-234","source":"Crossref","is-referenced-by-count":107,"title":["Asset pricing and portfolio selection based on\u00a0the\u00a0multivariate extended skew-Student-t distribution"],"prefix":"10.1007","volume":"176","author":[{"given":"C. J.","family":"Adcock","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,7,4]]},"reference":[{"key":"586_CR1","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1080\/13518470500039527","volume":"11","author":"C. J. Adcock","year":"2005","unstructured":"Adcock, C. J. (2005). Exploiting skewness to build an optimal Hedge fund with a currency overlay. The European Journal of Finance, 11, 445\u2013462.","journal-title":"The European Journal of Finance"},{"key":"586_CR2","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1080\/03610920601126084","volume":"36","author":"C. J. Adcock","year":"2007","unstructured":"Adcock, C. J. (2007). Extensions of Stein\u2019s lemma for the skew-normal distribution. Communications in Statistics \u2013 Theory and Methods, 36, 1661\u20131672.","journal-title":"Communications in Statistics \u2013 Theory and Methods"},{"key":"586_CR3","unstructured":"Adcock, C. J. (2008) Extensions of Stein\u2019s and Siegel\u2019s lemmas for the skew-Student distribution. Working paper."},{"key":"586_CR4","volume-title":"Financial modelling","author":"C. J. Adcock","year":"2001","unstructured":"Adcock, C. J., & Shutes, K. (2001). Portfolio selection based on the multivariate skew-normal distribution. In A. Skulimowski (Ed.), Financial modelling. Krakow: Progress and Business Publishers."},{"key":"586_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/13518470121786","volume":"7","author":"F. Aparicio","year":"2001","unstructured":"Aparicio, F., & Estrada, J. (2001). Empirical distributions of stock returns: European securities markets. European Journal of Finance, 7, 1\u201321.","journal-title":"European Journal of Finance"},{"key":"586_CR6","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1111\/j.1467-9469.2006.00503.x","volume":"33","author":"R. B. Arrellano-Valle","year":"2006","unstructured":"Arrellano-Valle, R. B., & Azzalini, A. (2006). On the unification of families of skew-normal distributions. Scandinavian Journal of Statistics, 33, 561\u2013574.","journal-title":"Scandinavian Journal of Statistics"},{"key":"586_CR7","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1002\/cjs.5550340403","volume":"34","author":"R. B. Arellano-Valle","year":"2006","unstructured":"Arellano-Valle, R. B., Branco, M. D., & Genton, M. G. (2006). A unified view on skewed distributions arising from selections. Canadian Journal of Statistics, 34, 581\u2013601.","journal-title":"Canadian Journal of Statistics"},{"key":"586_CR8","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.jmva.2004.10.002","volume":"96","author":"R. B. Arellano-Valle","year":"2005","unstructured":"Arellano-Valle, R. B., & Genton, M. G. (2005). On fundamental skew distributions. Journal of Multivariate Analysis, 96, 93\u2013116.","journal-title":"Journal of Multivariate Analysis"},{"key":"586_CR9","unstructured":"Arrellano-Valle, R. B., & Genton, M. G. (2008). Multivariate extended skew-t distributions and related families with applications. Technical report # 080628, Department of Econometrics, University of Geneva."},{"key":"586_CR10","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1111\/1467-9868.00391","volume":"65","author":"A. Azzalini","year":"2003","unstructured":"Azzalini, A., & Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of Royal Statistical Society Series B, 65, 367\u2013389.","journal-title":"Journal of Royal Statistical Society Series B"},{"key":"586_CR11","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1093\/biomet\/83.4.715","volume":"83","author":"A. Azzalini","year":"1996","unstructured":"Azzalini, A., & Dalla-Valle, A. (1996). The multivariate skew-normal distribution. Biometrika, 83, 715\u2013726.","journal-title":"Biometrika"},{"key":"586_CR12","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1111\/j.1751-5823.2007.00016.x","volume":"76","author":"A. Azzalini","year":"2008","unstructured":"Azzalini, A., & Genton, M. G. (2008). Robust likelihood methods based on the skew-t and related distributions. International Statistical Review, 76, 106\u2013129.","journal-title":"International Statistical Review"},{"key":"586_CR13","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1198\/073500104000000523","volume":"23","author":"L. Bauwens","year":"2005","unstructured":"Bauwens, L., & Laurent, S. (2005). A new class of multivariate skew densities, with applications to GARCH models. Journal of Business and Economic Statistics, 23, 346\u2013354.","journal-title":"Journal of Business and Economic Statistics"},{"key":"586_CR14","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316870","volume-title":"Bayesian theory","author":"J. M. Bernardo","year":"1994","unstructured":"Bernardo, J. M., & Smith, A. F. M. (1994). Bayesian theory. New York: Wiley."},{"key":"586_CR15","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1086\/295634","volume":"47","author":"R. Blattberg","year":"1974","unstructured":"Blattberg, R., & Gonedes, N. (1974). A comparison of the stable and Student distributions as statistical models for stock prices. Journal of Business, 47, 244\u2013280.","journal-title":"Journal of Business"},{"key":"586_CR16","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1006\/jmva.2000.1960","volume":"79","author":"M. D. Branco","year":"2001","unstructured":"Branco, M. D., & Dey, D. K. (2001). A general class of multivariate skew-elliptical distributions. Journal of Multivariate Analysis, 79, 99\u2013113.","journal-title":"Journal of Multivariate Analysis"},{"key":"586_CR17","doi-asserted-by":"crossref","DOI":"10.1002\/9781118673331","volume-title":"Copula methods in finance","author":"U. Cherubini","year":"2004","unstructured":"Cherubini, U., Luciano, E., & Vecchiato, W. (2004). Copula methods in finance. New York: Wiley."},{"key":"586_CR18","doi-asserted-by":"crossref","first-page":"383","DOI":"10.2307\/2325486","volume":"25","author":"E. Fama","year":"1970","unstructured":"Fama, E. (1970). Efficient capital markets: a review of theory and empirical work. Journal of Finance, 25, 383\u2013417.","journal-title":"Journal of Finance"},{"key":"586_CR19","series-title":"Monographs on statistics and applied probability","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-2937-2","volume-title":"Symmetric multivariate and related distributions","author":"K.-T. Fang","year":"1990","unstructured":"Fang, K.-T., Kotz, S., & Ng, K.-W. (1990). Symmetric multivariate and related distributions. Monographs on statistics and applied probability, Vol. 36. London: Chapman & Hall."},{"key":"586_CR20","doi-asserted-by":"crossref","DOI":"10.1201\/9780203492000","volume-title":"Skew-elliptical distributions and their applications: A journey beyond normality","author":"M. G. Genton","year":"2004","unstructured":"Genton, M. G. (2004). Skew-elliptical distributions and their applications: A journey beyond normality. Boca Raton: Chapman & Hall\/CRC Press."},{"key":"586_CR21","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.jspi.2003.09.008","volume":"126","author":"G. Gonz\u00e0lez-Far\u00edas","year":"2004","unstructured":"Gonz\u00e0lez-Far\u00edas, G., Dominguez-Mol\u00edna, A., & Gupta, A. K. (2004). Additive properties of skew normal random vectors. Journal of Statistical Planning and Inference, 126, 521\u2013534.","journal-title":"Journal of Statistical Planning and Inference"},{"key":"586_CR22","volume-title":"Distributions in statistics, continuous multivariate distributions","author":"N. L. Johnson","year":"1972","unstructured":"Johnson, N. L., & Kotz, S. (1972). Distributions in statistics, continuous multivariate distributions. New York: Wiley."},{"key":"586_CR23","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s184-002-8365-4","volume":"54","author":"M. C. Jones","year":"2001","unstructured":"Jones, M. C. (2001). Multivariate t and beta distributions associated with the multivariate F distribution. Metrika, 54, 215\u2013231.","journal-title":"Metrika"},{"key":"586_CR24","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1006\/jmva.2001.1993","volume":"81","author":"M. C. Jones","year":"2002","unstructured":"Jones, M. C. (2002). Marginal replacement in multivariate densities, with application to skewing spherically symmetric distributions. Journal of Multivariate Analysis, 81, 85\u201399.","journal-title":"Journal of Multivariate Analysis"},{"key":"586_CR25","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1111\/1467-9868.00378","volume":"65","author":"M. C. Jones","year":"2003","unstructured":"Jones, M. C., & Faddy, M. J. (2003). A skew extension of the t distribution, with applications. Journal of Royal Statistical Society Series B, 65, 159\u2013174.","journal-title":"Journal of Royal Statistical Society Series B"},{"key":"586_CR26","doi-asserted-by":"crossref","unstructured":"Harvey, C. R., Leichty, J. C., Leichty, M. W., & Muller, P. (2004). Portfolio selection with higher moments. Working paper.","DOI":"10.2139\/ssrn.634141"},{"key":"586_CR27","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.jmva.2004.10.007","volume":"94","author":"W. C. Horrace","year":"2005","unstructured":"Horrace, W. C. (2005). Some results on the multivariate truncated normal distribution. Journal of Multivariate Analysis, 94, 209\u2013221.","journal-title":"Journal of Multivariate Analysis"},{"key":"586_CR28","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1287\/mnsc.29.11.1257","volume":"11","author":"J. G. Kallberg","year":"1983","unstructured":"Kallberg, J. G., & Ziemba, W. T. (1983). Comparison of alternative functions in portfolio selection problems. Management Science, 11, 1257\u20131276.","journal-title":"Management Science"},{"key":"586_CR29","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1016\/j.spl.2005.11.004","volume":"76","author":"Z. Landsman","year":"2006","unstructured":"Landsman, Z. (2006). On the generalization of Stein\u2019s lemma for elliptical class of distributions. Statistics & Probability Letters, 76, 1012\u20131016.","journal-title":"Statistics & Probability Letters"},{"key":"586_CR30","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1016\/j.jmva.2007.05.006","volume":"99","author":"Z. Landsman","year":"2008","unstructured":"Landsman, Z., & Ne\u0161lehov\u00e1, J. (2008). Stein\u2019s lemma for elliptical random vectors. Journal of Multivariate Analysis, 99, 912\u2013927.","journal-title":"Journal of Multivariate Analysis"},{"key":"586_CR31","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0167-7152(94)90121-X","volume":"21","author":"J. S. Liu","year":"1994","unstructured":"Liu, J. S. (1994). Siegel\u2019s formula via Stein\u2019s identities. Statistics and Probability Letters, 21, 247\u2013251.","journal-title":"Statistics and Probability Letters"},{"key":"586_CR32","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/0304-4076(94)01612-4","volume":"66","author":"J. B. McDonald","year":"1995","unstructured":"McDonald, J. B., & Xu, Y. J. (1995). A generalization of the beta distribution with applications. Journal of Econometrics, 66, 133\u2013152.","journal-title":"Journal of Econometrics"},{"key":"586_CR33","unstructured":"Meucci, A. (2006). Beyond Black-Littermann: views on non-normal markets. Risk, February, 87\u201392."},{"key":"586_CR34","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1086\/295425","volume":"45","author":"P. Praetz","year":"1972","unstructured":"Praetz, P. (1972). The distribution of share price changes. Journal of Business, 45, 49\u201355.","journal-title":"Journal of Business"},{"key":"586_CR35","doi-asserted-by":"crossref","first-page":"129","DOI":"10.2307\/3316064","volume":"31","author":"S. K. Sahu","year":"2003","unstructured":"Sahu, S. K., Dey, D. K., & Branco, M. D. (2003). A new class of multivariate skew distributions with applications to Bayesian regression models. Canadian Journal of Statistics, 31, 129\u2013150.","journal-title":"Canadian Journal of Statistics"},{"key":"586_CR36","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1214\/aos\/1176345632","volume":"9","author":"C. Stein","year":"1981","unstructured":"Stein, C. (1981). Estimation of the mean of a multivariate normal distribution. Annals of Statistics, 9, 1135\u20131151.","journal-title":"Annals of Statistics"},{"key":"586_CR37","doi-asserted-by":"crossref","first-page":"1650","DOI":"10.1287\/mnsc.44.12.1650","volume":"44","author":"P. Theodossiou","year":"1998","unstructured":"Theodossiou, P. (1998). Financial data and the skewed generalised T distribution. Management Science, 44, 1650\u20131661.","journal-title":"Management Science"},{"key":"586_CR38","first-page":"131","volume":"44","author":"J. L. Treynor","year":"1966","unstructured":"Treynor, J. L., & Mazuy, K. (1966). Can mutual funds outguess the market? Harvard Business Review, 44, 131\u2013136.","journal-title":"Harvard Business Review"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-009-0586-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-009-0586-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-009-0586-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T14:07:55Z","timestamp":1559138875000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-009-0586-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7,4]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,4]]}},"alternative-id":["586"],"URL":"https:\/\/doi.org\/10.1007\/s10479-009-0586-4","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7,4]]}}}