{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T06:42:01Z","timestamp":1682491321109},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2013,6]]},"abstract":"<jats:p>In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent, identically distributed data. Under mild regularity conditions, we prove a law of large numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straightforward way to establish convergence with probability 1 of sample-based estimators of risk averse stochastic programming problems.<\/jats:p>","DOI":"10.1017\/s0021900200013541","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:51:01Z","timestamp":1459263061000},"page":"533-541","source":"Crossref","is-referenced-by-count":1,"title":["Consistency of Sample Estimates of Risk Averse Stochastic Programs"],"prefix":"10.1017","volume":"50","author":[{"given":"Alexander","family":"Shapiro","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,3,1]]},"reference":[{"key":"S0021900200013541_ref9","doi-asserted-by":"publisher","DOI":"10.1080\/10485250903060592"},{"key":"S0021900200013541_ref8","volume-title":"Lectures on Stochastic Programming: Modeling and Theory","year":"2009"},{"key":"S0021900200013541_ref7","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1050.0186"},{"key":"S0021900200013541_ref6","volume-title":"Variational Analysis","year":"1998"},{"key":"S0021900200013541_ref1","first-page":"1","volume":"2","year":"1996","journal-title":"J. Convex Anal"},{"key":"S0021900200013541_ref4","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176351052"},{"key":"S0021900200013541_ref3","volume-title":"Probability and Measure","year":"1995"},{"key":"S0021900200013541_ref2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00068"},{"key":"S0021900200013541_ref5","volume-title":"Stochastic Finance: An Introduction in Discrete Time","year":"2004"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200013541","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T06:21:20Z","timestamp":1682490080000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200013541\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6]]},"references-count":9,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2013,6]]}},"alternative-id":["S0021900200013541"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200013541","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6]]}}}