{"title":"扩展单调发电机设置中具有lsamvy跳变的BSDEs的存在唯一性及比较结果。","authors":"Christel Geiss, Alexander Steinicke","doi":"10.1186/s41546-018-0034-y","DOIUrl":null,"url":null,"abstract":"<p><p>We show that the comparison results for a backward SDE with jumps established in Royer (Stoch. Process. Appl 116: 1358-1376, 2006) and Yin and Mao (J. Math. Anal. Appl 346: 345-358, 2008) hold under more simplified conditions. Moreover, we prove existence and uniqueness allowing the coefficients in the linear growth- and monotonicity-condition for the generator to be random and time-dependent. In the <i>L</i> <sup>2</sup>-case with linear growth, this also generalizes the results of Kruse and Popier (Stochastics 88: 491-539, 2016). For the proof of the comparison result, we introduce an approximation technique: Given a BSDE driven by Brownian motion and Poisson random measure, we approximate it by BSDEs where the Poisson random measure admits only jumps of size larger than 1/<i>n</i>.</p>","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"3 1","pages":"9"},"PeriodicalIF":1.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s41546-018-0034-y","citationCount":"9","resultStr":"{\"title\":\"Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting.\",\"authors\":\"Christel Geiss, Alexander Steinicke\",\"doi\":\"10.1186/s41546-018-0034-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We show that the comparison results for a backward SDE with jumps established in Royer (Stoch. Process. Appl 116: 1358-1376, 2006) and Yin and Mao (J. Math. Anal. Appl 346: 345-358, 2008) hold under more simplified conditions. Moreover, we prove existence and uniqueness allowing the coefficients in the linear growth- and monotonicity-condition for the generator to be random and time-dependent. In the <i>L</i> <sup>2</sup>-case with linear growth, this also generalizes the results of Kruse and Popier (Stochastics 88: 491-539, 2016). For the proof of the comparison result, we introduce an approximation technique: Given a BSDE driven by Brownian motion and Poisson random measure, we approximate it by BSDEs where the Poisson random measure admits only jumps of size larger than 1/<i>n</i>.</p>\",\"PeriodicalId\":42330,\"journal\":{\"name\":\"Probability Uncertainty and Quantitative Risk\",\"volume\":\"3 1\",\"pages\":\"9\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1186/s41546-018-0034-y\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Uncertainty and Quantitative Risk\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s41546-018-0034-y\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2018/12/28 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability Uncertainty and Quantitative Risk","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s41546-018-0034-y","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/12/28 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting.
We show that the comparison results for a backward SDE with jumps established in Royer (Stoch. Process. Appl 116: 1358-1376, 2006) and Yin and Mao (J. Math. Anal. Appl 346: 345-358, 2008) hold under more simplified conditions. Moreover, we prove existence and uniqueness allowing the coefficients in the linear growth- and monotonicity-condition for the generator to be random and time-dependent. In the L2-case with linear growth, this also generalizes the results of Kruse and Popier (Stochastics 88: 491-539, 2016). For the proof of the comparison result, we introduce an approximation technique: Given a BSDE driven by Brownian motion and Poisson random measure, we approximate it by BSDEs where the Poisson random measure admits only jumps of size larger than 1/n.
期刊介绍：
Probability, Uncertainty and Quantitative Risk (PUQR) is a quarterly academic journal under the supervision of the Ministry of Education of the People's Republic of China and hosted by Shandong University, which is open to the public at home and abroad (ISSN 2095-9672; CN 37-1505/O1).
Probability, Uncertainty and Quantitative Risk (PUQR) mainly reports on the major developments in modern probability theory, covering stochastic analysis and statistics, stochastic processes, dynamical analysis and control theory, and their applications in the fields of finance, economics, biology, and computer science. The journal is currently indexed in ESCI, Scopus, Mathematical Reviews, zbMATH Open and other databases.
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