Pub Date : 2016-12-01DOI: 10.1186/S41546-016-0007-Y
Dejian Chang, Huili Liu, J. Xiong
{"title":"A branching particle system approximation for a class of FBSDEs","authors":"Dejian Chang, Huili Liu, J. Xiong","doi":"10.1186/S41546-016-0007-Y","DOIUrl":"https://doi.org/10.1186/S41546-016-0007-Y","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"62 1","pages":"1-34"},"PeriodicalIF":1.5,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89356115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Unbiased estimation for parameters of maximal distribution is a fundamental problem in the statistical theory of sublinear expectations. In this paper, we proved that the maximum estimator is the largest unbiased estimator for the upper mean and the minimum estimator is the smallest unbiased estimator for the lower mean.
{"title":"Optimal unbiased estimation for maximal distribution","authors":"Hanqing Jin, S. Peng","doi":"10.3934/puqr.2021009","DOIUrl":"https://doi.org/10.3934/puqr.2021009","url":null,"abstract":"Unbiased estimation for parameters of maximal distribution is a fundamental problem in the statistical theory of sublinear expectations. In this paper, we proved that the maximum estimator is the largest unbiased estimator for the upper mean and the minimum estimator is the smallest unbiased estimator for the lower mean.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"61 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2016-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73817287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs) with jumps, where path-dependence means the dependence of the free term and generator of a path of a càdlàg process. Furthermore, we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation (FSVIE) with jumps and a linear path-dependent BSVIE with jumps. As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.
{"title":"Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle","authors":"L. Overbeck, J. Röder","doi":"10.2139/ssrn.2836961","DOIUrl":"https://doi.org/10.2139/ssrn.2836961","url":null,"abstract":"We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs) with jumps, where path-dependence means the dependence of the free term and generator of a path of a càdlàg process. Furthermore, we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation (FSVIE) with jumps and a linear path-dependent BSVIE with jumps. As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"112 1","pages":"1-37"},"PeriodicalIF":1.5,"publicationDate":"2016-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80121542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-08-16DOI: 10.1186/S41546-016-0005-0
Y. Kutoyants
{"title":"On approximation of BSDE and multi-step MLE-processes","authors":"Y. Kutoyants","doi":"10.1186/S41546-016-0005-0","DOIUrl":"https://doi.org/10.1186/S41546-016-0005-0","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"16 1","pages":"1-22"},"PeriodicalIF":1.5,"publicationDate":"2016-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73297844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-07-12DOI: 10.1186/S41546-017-0025-4
A. Papapantoleon, Robert Wardenga
{"title":"Continuous tenor extension of affine LIBOR models with multiple curves and applications to XVA","authors":"A. Papapantoleon, Robert Wardenga","doi":"10.1186/S41546-017-0025-4","DOIUrl":"https://doi.org/10.1186/S41546-017-0025-4","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"66 1","pages":"1-28"},"PeriodicalIF":1.5,"publicationDate":"2016-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86420338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-07-10DOI: 10.1186/S41546-018-0029-8
Y. Jiao, Idris Kharroubi
{"title":"Information uncertainty related to marked random times and optimal investment","authors":"Y. Jiao, Idris Kharroubi","doi":"10.1186/S41546-018-0029-8","DOIUrl":"https://doi.org/10.1186/S41546-018-0029-8","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"5 1","pages":"1-24"},"PeriodicalIF":1.5,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81807882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-06-01DOI: 10.1186/s41546-020-00046-x
Samuel N. Cohen
{"title":"Uncertainty and filtering of hidden Markov models in discrete time","authors":"Samuel N. Cohen","doi":"10.1186/s41546-020-00046-x","DOIUrl":"https://doi.org/10.1186/s41546-020-00046-x","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"3 1","pages":"1-34"},"PeriodicalIF":1.5,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86777345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-04-22DOI: 10.1186/S41546-016-0008-X
H. Pham
{"title":"Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications","authors":"H. Pham","doi":"10.1186/S41546-016-0008-X","DOIUrl":"https://doi.org/10.1186/S41546-016-0008-X","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"44 1","pages":"1-26"},"PeriodicalIF":1.5,"publicationDate":"2016-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89236778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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