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Probability Uncertainty and Quantitative Risk最新文献

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The Cauchy problem of Backward Stochastic Super-Parabolic Equations with Quadratic Growth 具有二次增长的倒向随机超抛物型方程的Cauchy问题
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2019-12-01 DOI: 10.1186/S41546-019-0037-3
Renzhi Qiu, Shanjian Tang
{"title":"The Cauchy problem of Backward Stochastic Super-Parabolic Equations with Quadratic Growth","authors":"Renzhi Qiu, Shanjian Tang","doi":"10.1186/S41546-019-0037-3","DOIUrl":"https://doi.org/10.1186/S41546-019-0037-3","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"14 1","pages":"1-29"},"PeriodicalIF":1.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84540838","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}
引用次数: 0
General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition 具有满足弱随机单调条件的一般时间间隔多维BSDEs
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2019-11-25 DOI: 10.3934/puqr.2021015
Tingting Li, Ziheng Xu, Shengjun Fan
{"title":"General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition","authors":"Tingting Li, Ziheng Xu, Shengjun Fan","doi":"10.3934/puqr.2021015","DOIUrl":"https://doi.org/10.3934/puqr.2021015","url":null,"abstract":"<p style='text-indent:20px;'>This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator <inline-formula> <tex-math id=\"M1\">begin{document}$ g $end{document}</tex-math> </inline-formula> satisfies a weak stochastic-monotonicity condition and a general growth condition in the state variable <inline-formula> <tex-math id=\"M2\">begin{document}$ y $end{document}</tex-math> </inline-formula>, and a stochastic-Lipschitz condition in the state variable <inline-formula> <tex-math id=\"M3\">begin{document}$ z $end{document}</tex-math> </inline-formula>. This unifies and strengthens some known works. In order to prove this result, we develop some ideas and techniques employed in Xiao and Fan [<xref ref-type=\"bibr\" rid=\"b25\">25</xref>] and Liu et al. [<xref ref-type=\"bibr\" rid=\"b15\">15</xref>]. In particular, we put forward and prove a stochastic Gronwall-type inequality and a stochastic Bihari-type inequality, which generalize the classical ones and may be useful in other applications. The martingale representation theorem, Itô’s formula, and the BMO martingale tool are used to prove these two inequalities. </p>","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"62 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78552676","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}
引用次数: 1
Dual representation of expectile-based expected shortfall and its properties 基于期望差的对偶表示及其性质
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2019-11-08 DOI: 10.3934/puqr.2021005
Samuel Drapeau, Mekonnen Tadese
{"title":"Dual representation of expectile-based expected shortfall and its properties","authors":"Samuel Drapeau, Mekonnen Tadese","doi":"10.3934/puqr.2021005","DOIUrl":"https://doi.org/10.3934/puqr.2021005","url":null,"abstract":"An expectile can be considered a generalization of a quantile. While expected shortfall is a quantile-based risk measure, we study its counterpart—the expectile-based expected shortfall—where expectile takes the place of a quantile. We provide its dual representation in terms of a Bochner integral. Among other properties, we show that it is bounded from below in terms of the convex combination of expected shortfalls, and also from above by the smallest law invariant, coherent, and comonotonic risk measures, for which we give the explicit formulation of the corresponding distortion function. As a benchmark to the industry standard expected shortfall, we further provide its comparative asymptotic behavior in terms of extreme value distributions. Based on these results, we finally explicitly compute the expectile-based expected shortfall for selected classes of distributions.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"29 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90609911","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}
引用次数: 1
Publisher Correction to: Probability, uncertainty and quantitative risk, volume 4 出版商更正:概率，不确定性和定量风险，卷4
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2019-08-26 DOI: 10.1186/s41546-019-0041-7
Uncertainty and Quantitative Risk Probability
{"title":"Publisher Correction to: Probability, uncertainty and quantitative risk, volume 4","authors":"Uncertainty and Quantitative Risk Probability","doi":"10.1186/s41546-019-0041-7","DOIUrl":"https://doi.org/10.1186/s41546-019-0041-7","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"87 1","pages":"1"},"PeriodicalIF":1.5,"publicationDate":"2019-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83437438","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}
引用次数: 0
Stein’s method for the law of large numbers under sublinear expectations 斯坦在次线性期望下的大数定律的方法
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2019-04-09 DOI: 10.3934/puqr.2021010
Yongsheng Song
{"title":"Stein’s method for the law of large numbers under sublinear expectations","authors":"Yongsheng Song","doi":"10.3934/puqr.2021010","DOIUrl":"https://doi.org/10.3934/puqr.2021010","url":null,"abstract":"<p style='text-indent:20px;'>Peng, S. [<xref ref-type=\"bibr\" rid=\"b6\">6</xref>] proved the law of large numbers under a sublinear expectation. In this paper, we give its error estimates by Stein’s method. </p>","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76956340","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}
引用次数: 11
Efficient hedging under ambiguity in continuous time 连续时间模糊性下的有效对冲
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2018-12-27 DOI: 10.1186/s41546-020-00048-9
Ludovic Tangpi
{"title":"Efficient hedging under ambiguity in continuous time","authors":"Ludovic Tangpi","doi":"10.1186/s41546-020-00048-9","DOIUrl":"https://doi.org/10.1186/s41546-020-00048-9","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"125 1","pages":"1-19"},"PeriodicalIF":1.5,"publicationDate":"2018-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75929683","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}
引用次数: 0
Harnack inequality and gradient estimate for functional G-SDEs with degenerate noise 带退化噪声的泛函G-SDEs的harack不等式和梯度估计
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2018-12-11 DOI: 10.3934/puqr.2022008
Xing Huang, Fen-Fen Yang
{"title":"Harnack inequality and gradient estimate for functional G-SDEs with degenerate noise","authors":"Xing Huang, Fen-Fen Yang","doi":"10.3934/puqr.2022008","DOIUrl":"https://doi.org/10.3934/puqr.2022008","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"28 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2018-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83126279","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}
引用次数: 2
Nonlinear regression without i.i.d. assumption 无i.i.d假设的非线性回归
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2018-11-23 DOI: 10.1186/s41546-019-0042-6
Qing Xu, Xiaohua Xuan
{"title":"Nonlinear regression without i.i.d. assumption","authors":"Qing Xu, Xiaohua Xuan","doi":"10.1186/s41546-019-0042-6","DOIUrl":"https://doi.org/10.1186/s41546-019-0042-6","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"114 1","pages":"1-15"},"PeriodicalIF":1.5,"publicationDate":"2018-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78958864","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}
引用次数: 6
Convergence of the deep BSDE method for coupled FBSDEs 耦合fbsde的深度BSDE方法的收敛性
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2018-11-03 DOI: 10.1186/s41546-020-00047-w
Jiequn Han, Jihao Long
{"title":"Convergence of the deep BSDE method for coupled FBSDEs","authors":"Jiequn Han, Jihao Long","doi":"10.1186/s41546-020-00047-w","DOIUrl":"https://doi.org/10.1186/s41546-020-00047-w","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"31 1","pages":"1-33"},"PeriodicalIF":1.5,"publicationDate":"2018-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73957029","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}
引用次数: 108
Affine processes under parameter uncertainty 参数不确定下的仿射过程
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2018-06-07 DOI: 10.1186/s41546-019-0039-1
T. Fadina, Ariel Neufeld, Thorsten Schmidt
{"title":"Affine processes under parameter uncertainty","authors":"T. Fadina, Ariel Neufeld, Thorsten Schmidt","doi":"10.1186/s41546-019-0039-1","DOIUrl":"https://doi.org/10.1186/s41546-019-0039-1","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"04 1","pages":"1-35"},"PeriodicalIF":1.5,"publicationDate":"2018-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85956049","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}
引用次数: 34
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