{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:05:55Z","timestamp":1760234755872,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,11]],"date-time":"2021-06-11T00:00:00Z","timestamp":1623369600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 11771343"],"award-info":[{"award-number":["No. 11771343"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we study the dynamic risk measures for processes induced by backward stochastic differential equations driven by Teugel\u2019s martingales associated with L\u00e9vy processes (BSDELs). The representation theorem for generators of BSDELs is provided. Furthermore, the time consistency of the coherent and convex dynamic risk measures for processes is characterized by means of the generators of BSDELs. Moreover, the coherency and convexity of dynamic risk measures for processes are characterized by the generators of BSDELs. Finally, we provide two numerical examples to illustrate the proposed dynamic risk measures.<\/jats:p>","DOI":"10.3390\/e23060741","type":"journal-article","created":{"date-parts":[[2021,6,11]],"date-time":"2021-06-11T12:44:37Z","timestamp":1623415477000},"page":"741","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Dynamic Risk Measures for Processes via Backward Stochastic Differential Equations Associated with L\u00e9vy Processes"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4319-5317","authenticated-orcid":false,"given":"Liangliang","family":"Miao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1693-0646","authenticated-orcid":false,"given":"Zhang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Jiangxi Agricultural University, Nanchang 330045, China"}]},{"given":"Yijun","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,11]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"BSDE associated with l\u00e9vy processes and application to PDIE","volume":"16","author":"Bahlali","year":"2003","journal-title":"J. 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