Pub Date : 2016-03-29DOI: 10.1186/s41546-017-0012-9
T. Bielecki, Igor Cialenco, Marcin Pitera
{"title":"A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective","authors":"T. Bielecki, Igor Cialenco, Marcin Pitera","doi":"10.1186/s41546-017-0012-9","DOIUrl":"https://doi.org/10.1186/s41546-017-0012-9","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"28 1","pages":"1-52"},"PeriodicalIF":1.5,"publicationDate":"2016-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86239777","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 : 2016-02-29DOI: 10.1186/s41546-017-0022-7
Qi Lü, Tianxiao Wang, Xu Zhang
{"title":"Characterization of optimal feedback for stochastic linear quadratic control problems","authors":"Qi Lü, Tianxiao Wang, Xu Zhang","doi":"10.1186/s41546-017-0022-7","DOIUrl":"https://doi.org/10.1186/s41546-017-0022-7","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"48 1","pages":"1-20"},"PeriodicalIF":1.5,"publicationDate":"2016-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91277772","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 : 2016-02-25DOI: 10.1186/s41546-016-0002-3
Xunjing Li, Jingrui Sun, J. Yong
{"title":"Mean-field stochastic linear quadratic optimal control problems: closed-loop solvability","authors":"Xunjing Li, Jingrui Sun, J. Yong","doi":"10.1186/s41546-016-0002-3","DOIUrl":"https://doi.org/10.1186/s41546-016-0002-3","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"3 1","pages":"1-24"},"PeriodicalIF":1.5,"publicationDate":"2016-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88889387","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}
Allowing for correlated squared returns across two consecutive periods, portfolio theory for two periods is developed. This correlation makes it necessary to work with non-Gaussian models. The two-period conic portfolio problem is formulated and implemented. This development leads to a mean ask price frontier, where the latter employs concave distortions. The modeling permits access to skewness via randomized drifts. Optimal portfolios maximize a conservative market value seen as a bid price for the portfolio. On the mean ask price frontier we observe a tradeoff between the deterministic and random drifts and the volatility costs of increasing the deterministic drift. From a historical perspective, we also implement a mean-variance analysis. The resulting mean-variance frontier is three-dimensional expressing the minimal variance as a function of the targeted levels for the deterministic and random drift.
{"title":"Portfolio theory for squared returns correlated across time","authors":"E. Eberlein, D. Madan","doi":"10.2139/ssrn.2635632","DOIUrl":"https://doi.org/10.2139/ssrn.2635632","url":null,"abstract":"Allowing for correlated squared returns across two consecutive periods, portfolio theory for two periods is developed. This correlation makes it necessary to work with non-Gaussian models. The two-period conic portfolio problem is formulated and implemented. This development leads to a mean ask price frontier, where the latter employs concave distortions. The modeling permits access to skewness via randomized drifts. Optimal portfolios maximize a conservative market value seen as a bid price for the portfolio. On the mean ask price frontier we observe a tradeoff between the deterministic and random drifts and the volatility costs of increasing the deterministic drift. From a historical perspective, we also implement a mean-variance analysis. The resulting mean-variance frontier is three-dimensional expressing the minimal variance as a function of the targeted levels for the deterministic and random drift.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"19 1","pages":"1-36"},"PeriodicalIF":1.5,"publicationDate":"2016-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88688116","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 : 2015-10-30DOI: 10.1186/s41546-016-0003-2
A. Schied, Iryna Voloshchenko
{"title":"Pathwise no-arbitrage in a class of Delta hedging strategies","authors":"A. Schied, Iryna Voloshchenko","doi":"10.1186/s41546-016-0003-2","DOIUrl":"https://doi.org/10.1186/s41546-016-0003-2","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"55 1","pages":"1-25"},"PeriodicalIF":1.5,"publicationDate":"2015-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90910303","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 : 2015-07-27DOI: 10.1186/s41546-017-0013-8
Zhengyan Lin, Li-Xin Zhang
{"title":"Convergence to a self-normalized G-Brownian motion","authors":"Zhengyan Lin, Li-Xin Zhang","doi":"10.1186/s41546-017-0013-8","DOIUrl":"https://doi.org/10.1186/s41546-017-0013-8","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"1 1","pages":"1-25"},"PeriodicalIF":1.5,"publicationDate":"2015-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86859259","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 : 2015-01-28DOI: 10.1186/s41546-020-00049-8
R. Buckdahn, C. Keller, Jin Ma, Jianfeng Zhang
{"title":"Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions","authors":"R. Buckdahn, C. Keller, Jin Ma, Jianfeng Zhang","doi":"10.1186/s41546-020-00049-8","DOIUrl":"https://doi.org/10.1186/s41546-020-00049-8","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"30 1","pages":"1-59"},"PeriodicalIF":1.5,"publicationDate":"2015-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83780840","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 : 2014-02-13DOI: 10.1186/s41546-018-0033-z
F. Biagini, T. Meyer-Brandis, B. Øksendal, K. Paczka
{"title":"Optimal control with delayed information flow of systems driven by G-Brownian motion","authors":"F. Biagini, T. Meyer-Brandis, B. Øksendal, K. Paczka","doi":"10.1186/s41546-018-0033-z","DOIUrl":"https://doi.org/10.1186/s41546-018-0033-z","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"46 1","pages":"1-24"},"PeriodicalIF":1.5,"publicationDate":"2014-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78850542","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}
In this paper, we extend the definition of conditional begin{document}$ G{text{-}}{rm{expectation}} $end{document} to a larger space on which the dynamical consistency still holds. We can consistently define, by taking the limit, the conditional begin{document}$ G{text{-}}{rm{expectation}} $end{document} for each random variable begin{document}$ X $end{document}, which is the downward limit (respectively, upward limit) of a monotone sequence begin{document}$ {X_{i}} $end{document} in begin{document}$ L_{G}^{1}(Omega) $end{document}. To accomplish this procedure, some careful analysis is needed. Moreover, we present a suitable definition of stopping times and obtain the optional stopping theorem. We also provide some basic and interesting properties for the extended conditional begin{document}$ G{text{-}}{rm{expectation}} $end{document}.
In this paper, we extend the definition of conditional begin{document}$ G{text{-}}{rm{expectation}} $end{document} to a larger space on which the dynamical consistency still holds. We can consistently define, by taking the limit, the conditional begin{document}$ G{text{-}}{rm{expectation}} $end{document} for each random variable begin{document}$ X $end{document} , which is the downward limit (respectively, upward limit) of a monotone sequence begin{document}$ {X_{i}} $end{document} in begin{document}$ L_{G}^{1}(Omega) $end{document} . To accomplish this procedure, some careful analysis is needed. Moreover, we present a suitable definition of stopping times and obtain the optional stopping theorem. We also provide some basic and interesting properties for the extended conditional begin{document}$ G{text{-}}{rm{expectation}} $end{document} .
{"title":"Extended conditional G-expectations and related stopping times","authors":"Mingshang Hu, S. Peng","doi":"10.3934/puqr.2021018","DOIUrl":"https://doi.org/10.3934/puqr.2021018","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we extend the definition of conditional <inline-formula> <tex-math id=\"M2\">begin{document}$ G{text{-}}{rm{expectation}} $end{document}</tex-math> </inline-formula> to a larger space on which the dynamical consistency still holds. We can consistently define, by taking the limit, the conditional <inline-formula> <tex-math id=\"M3\">begin{document}$ G{text{-}}{rm{expectation}} $end{document}</tex-math> </inline-formula> for each random variable <inline-formula> <tex-math id=\"M4\">begin{document}$ X $end{document}</tex-math> </inline-formula>, which is the downward limit (respectively, upward limit) of a monotone sequence <inline-formula> <tex-math id=\"M5\">begin{document}$ {X_{i}} $end{document}</tex-math> </inline-formula> in <inline-formula> <tex-math id=\"M6\">begin{document}$ L_{G}^{1}(Omega) $end{document}</tex-math> </inline-formula>. To accomplish this procedure, some careful analysis is needed. Moreover, we present a suitable definition of stopping times and obtain the optional stopping theorem. We also provide some basic and interesting properties for the extended conditional <inline-formula> <tex-math id=\"M7\">begin{document}$ G{text{-}}{rm{expectation}} $end{document}</tex-math> </inline-formula>. </p>","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"8 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2013-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85313268","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 introduce G-Levy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations. We then obtain the Levy-Khintchine formula and the existence for G-Levy processes. We also introduce G-Poisson processes.
{"title":"G-Lévy processes under sublinear expectations","authors":"Mingshang Hu, S. Peng","doi":"10.3934/PUQR.2021001","DOIUrl":"https://doi.org/10.3934/PUQR.2021001","url":null,"abstract":"We introduce G-Levy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations. We then obtain the Levy-Khintchine formula and the existence for G-Levy processes. We also introduce G-Poisson processes.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"16 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2009-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78403985","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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