{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T02:34:44Z","timestamp":1773974084895,"version":"3.50.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2017,3,27]],"date-time":"2017-03-27T00:00:00Z","timestamp":1490572800000},"content-version":"unspecified","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":[[2018,7]]},"DOI":"10.1007\/s10479-017-2469-4","type":"journal-article","created":{"date-parts":[[2017,3,27]],"date-time":"2017-03-27T03:55:29Z","timestamp":1490586929000},"page":"199-221","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Robust risk budgeting"],"prefix":"10.1007","volume":"266","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0265-5556","authenticated-orcid":false,"given":"Michalis","family":"Kapsos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicos","family":"Christofides","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Berc","family":"Rustem","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,3,27]]},"reference":[{"key":"2469_CR1","unstructured":"Appell, D. (2009). Bridgewater under the weather. Pensions and Investements."},{"key":"2469_CR2","doi-asserted-by":"crossref","unstructured":"Artzner, P., Delbaen, F., Eber, J. M. & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203\u2013228.","DOI":"10.1111\/1467-9965.00068"},{"key":"2469_CR3","doi-asserted-by":"crossref","unstructured":"Asness, C., Frazzini, A., & Pedersen, L. (2012). Leverage aversion and risk parity. Financial Analysts Journal, 68(1), 47\u201359.","DOI":"10.2469\/faj.v68.n1.1"},{"issue":"1","key":"2469_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/rfs\/13.1.1","volume":"13","author":"G Bekaert","year":"2000","unstructured":"Bekaert, G., & Wu, G. (2000). Asymmetric volatility and risk in equity markets. The Review of Financial Studies, 13(1), 1\u201342.","journal-title":"The Review of Financial Studies"},{"issue":"2","key":"2469_CR5","doi-asserted-by":"crossref","first-page":"7","DOI":"10.3905\/jfi.1991.408013","volume":"1","author":"F Black","year":"1991","unstructured":"Black, F., & Litterman, R. (1991). Asset allocation: Combining investor views with market equilibrium. Journal of Fixed Income, 1(2), 7\u201318.","journal-title":"Journal of Fixed Income"},{"key":"2469_CR6","doi-asserted-by":"crossref","first-page":"28","DOI":"10.2469\/faj.v48.n5.28","volume":"48","author":"F Black","year":"1992","unstructured":"Black, F., & Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48, 28\u201343.","journal-title":"Financial Analysts Journal"},{"issue":"3","key":"2469_CR7","doi-asserted-by":"crossref","first-page":"39","DOI":"10.21314\/JOR.2013.258","volume":"15","author":"K Boudt","year":"2012","unstructured":"Boudt, K., Carl, P., & Peterson, B. G. (2012). Asset allocation with conditional value-at-risk budgets. Journal of Risk, 15(3), 39\u201368.","journal-title":"Journal of Risk"},{"key":"2469_CR8","doi-asserted-by":"crossref","unstructured":"Bruder, B., & Roncalli, T. (2012). Managing risk exposures using the risk budgeting approach. Working Paper, Lyxor.","DOI":"10.2139\/ssrn.2009778"},{"key":"2469_CR9","unstructured":"Chaves, D.\u00a0B., Hsu, J.\u00a0C., Li, F., & Shakernia, O. (2011). Parity portfolio vs. other asset allocation heuristic portfolios. Journal of Investing, 20(1), 108\u2013118."},{"issue":"2","key":"2469_CR10","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/S0005-1098(98)00150-2","volume":"35","author":"J Darlington","year":"1999","unstructured":"Darlington, J., Pantelides, C. C., & Rustem, B. (1999). An algorithm for constrained nonlinear optimization under uncertainty. Automatica, 35(2), 217\u2013228.","journal-title":"Automatica"},{"key":"2469_CR11","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1287\/mnsc.1080.0986","volume":"55","author":"V DeMiguel","year":"2009","unstructured":"DeMiguel, V., Garlappi, L., Nogales, F. J., & Uppal, R. (2009a). A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms. Management Science, 55, 798\u2013812.","journal-title":"Management Science"},{"issue":"5","key":"2469_CR12","doi-asserted-by":"crossref","first-page":"1915","DOI":"10.1093\/rfs\/hhm075","volume":"22","author":"V DeMiguel","year":"2009","unstructured":"DeMiguel, V., Garlappi, L., & Uppal, R. (2009b). Optimal versus naive diversification: How inefficient is the 1\/n portfolio strategy? Review of Financial Studies, 22(5), 1915\u20131953.","journal-title":"Review of Financial Studies"},{"key":"2469_CR13","unstructured":"Downing, C., Madhavan, A., Singh, A., & Ulitsky, A. (2015). Portfolio construction and tail risk. Working Paper."},{"key":"2469_CR14","unstructured":"Jensen, M.\u00a0C., Black, F., & Scholes, M.\u00a0S. (1972). The capital asset pricing model: Some empirical tests. In M. C. Jensen (Ed.), Studies in the theory of capital markets. New York: Praeger. Available at SSRN: \n                        https:\/\/ssrn.com\/abstract=908569\n                        \n                    ."},{"issue":"2","key":"2469_CR15","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.ejor.2013.04.025","volume":"234","author":"M Kapsos","year":"2014","unstructured":"Kapsos, M., Christofides, N., & Rustem, B. (2014). Worst-case robust omega ratio. European Journal of Operational Research, 234(2), 499\u2013507. (Special Edition: 60 years following Harry Markowitz\u2019s contribution to portfolio theory and operations research).","journal-title":"European Journal of Operational Research"},{"issue":"4","key":"2469_CR16","doi-asserted-by":"crossref","first-page":"49","DOI":"10.21314\/JCF.2014.283","volume":"17","author":"M Kapsos","year":"2014","unstructured":"Kapsos, M., Zymler, S., Christofides, N., & Rustem, B. (2014b). Optimizing omega ratio using linear programming. Journal of Computational Finance, 17(4), 49\u201357.","journal-title":"Journal of Computational Finance"},{"issue":"4","key":"2469_CR17","doi-asserted-by":"crossref","first-page":"60","DOI":"10.3905\/jpm.2010.36.4.060","volume":"36","author":"S Maillard","year":"2010","unstructured":"Maillard, S., Roncalli, T., & Te\u00efletche, J. (2010). The properties of equally weighted risk contribution portfolios. The Journal of Portfolio Management, 36(4), 60\u201370.","journal-title":"The Journal of Portfolio Management"},{"issue":"1","key":"2469_CR18","first-page":"77","volume":"7","author":"H Markowitz","year":"1952","unstructured":"Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77\u201391.","journal-title":"The Journal of Finance"},{"key":"2469_CR19","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/0304-405X(80)90007-0","volume":"8","author":"R Merton","year":"1980","unstructured":"Merton, R. (1980). On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics, 8, 323\u2013361.","journal-title":"Journal of Financial Economics"},{"issue":"2","key":"2469_CR20","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/PL00011396","volume":"89","author":"W Ogryczak","year":"2001","unstructured":"Ogryczak, W., & Ruszczy\u0144ski, A. (2001). On consistency of stochastic dominance and mean-semideviation models. Mathematical Programming, 89(2), 217\u2013232.","journal-title":"Mathematical Programming"},{"issue":"3","key":"2469_CR21","doi-asserted-by":"crossref","first-page":"21","DOI":"10.21314\/JOR.2000.038","volume":"2","author":"RT Rockafellar","year":"2000","unstructured":"Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2(3), 21\u201342.","journal-title":"Journal of Risk"},{"issue":"1","key":"2469_CR22","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s00780-005-0165-8","volume":"10","author":"RT Rockafellar","year":"2006","unstructured":"Rockafellar, R. T., Uryasev, S., & Zabarankin, M. (2006). Generalized deviations in risk analysis. Finance and Stochastics, 10(1), 51\u201374.","journal-title":"Finance and Stochastics"},{"key":"2469_CR23","volume-title":"Introduction to risk parity and budgeting","author":"T Roncalli","year":"2013","unstructured":"Roncalli, T. (2013). Introduction to risk parity and budgeting. Boca Raton: CRC Press."},{"key":"2469_CR24","doi-asserted-by":"crossref","first-page":"49","DOI":"10.3905\/jpm.1994.409501","volume":"21","author":"WF Sharpe","year":"1994","unstructured":"Sharpe, W. F. (1994). The sharpe ratio. Journal of Portfolio Management, 21, 49\u201358.","journal-title":"Journal of Portfolio Management"},{"key":"2469_CR25","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1023\/B:ANOR.0000045281.41041.ed","volume":"132","author":"RH T\u00fct\u00fcnc\u00fc","year":"2004","unstructured":"T\u00fct\u00fcnc\u00fc, R. H., & Koenig, M. (2004). Robust asset allocation. Annals of Operations Research, 132, 157\u2013187.","journal-title":"Annals of Operations Research"},{"key":"2469_CR26","doi-asserted-by":"crossref","unstructured":"Viceira, L.\u00a0M. (2007). Life-cycle funds. Harvard Business School, Harvard University, Working Paper.","DOI":"10.2139\/ssrn.988362"},{"issue":"1","key":"2469_CR27","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1023\/B:ANOR.0000004764.76984.30","volume":"124","author":"S Zakovic","year":"2003","unstructured":"Zakovic, S., & Rustem, B. (2003). Semi-infinite programming and applications to minimax problems. Annals of Operations Research, 124(1), 81\u2013110.","journal-title":"Annals of Operations Research"},{"key":"2469_CR28","doi-asserted-by":"crossref","unstructured":"Zhu, S., & Fukushima, M. (2009). Worst-case conditional value-at-risk with application to robust portfolio management. Operations Research, 57(5), 1155\u20131168.","DOI":"10.1287\/opre.1080.0684"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-017-2469-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-017-2469-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-017-2469-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,5,31]],"date-time":"2018-05-31T10:00:37Z","timestamp":1527760837000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-017-2469-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,27]]},"references-count":28,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["2469"],"URL":"https:\/\/doi.org\/10.1007\/s10479-017-2469-4","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,27]]}}}