The Experts below are selected from a list of 36447 Experts worldwide ranked by ideXlab platform
Xueying Zhang - One of the best experts on this subject based on the ideXlab platform.
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atomic decompositions of banach lattice valued Martingales
Statistics & Probability Letters, 2012Co-Authors: Xueying Zhang, Chuanzhou ZhangAbstract:In this paper, atomic decompositions of Banach lattice-valued Martingales are given. We discuss the relation between the LERMT property and atomic decompositions. With the help of atomic decompositions, the relation of the Martingale spaces is investigated.
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atomic decompositions of banach lattice valued Martingales with weighted measure
Scientia Sinica Mathematica, 2012Co-Authors: Chuanzhou Zhang, Xueying ZhangAbstract:In this paper the atomic decompositions of Banach lattice-valued Martingales with weighted measure are given. With the help of the atomic decompositions, the interpolation theorems on Martingale spaces are investigated.
Nizar Touzi - One of the best experts on this subject based on the ideXlab platform.
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tightness and duality of Martingale transport on the skorokhod space
Stochastic Processes and their Applications, 2017Co-Authors: Gaoyue Guo, Xiaolu Tan, Nizar TouziAbstract:The Martingale optimal transport aims to optimally transfer a probability measure to another along the class of Martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which turns out to be the corresponding Kantorovich dual. In this paper we consider the continuous-time Martingale transport on the Skorokhod space of c`adi ag paths. Similar to the classical setting of optimal transport, we introduce different dual problems and establish the corresponding dualities by a crucial use of the S−topology and the dynamic programming principle 1 .
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optimal skorokhod embedding given full marginals and azema yor peacocks
Annals of Applied Probability, 2017Co-Authors: Sigrid Kallblad, Xiaolu Tan, Nizar TouziAbstract:We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval $[0,1]$. The problem is related to the study of extremal Martingales associated with a peacock (“process increasing in convex order,” by Hirsch, Profeta, Roynette and Yor [Peacocks and Associated Martingales, with Explicit Constructions (2011), Springer, Milan]). A general duality result is obtained by convergence techniques. We then study the case where the reward function depends on the maximum of the embedding process, which is the limit of the Martingale transport problem studied in Henry-Labordere, Obloj, Spoida and Touzi [Ann. Appl. Probab. 26 (2016) 1–44]. Under technical conditions, we then characterize the optimal value and the solution to the dual problem. In particular, the optimal embedding corresponds to the Madan and Yor [Bernoulli 8 (2002) 509–536] peacock under their “increasing mean residual value” condition. We also discuss the associated Martingale inequality.
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optimal skorokhod embedding given full marginals and azema yor peacocks
arXiv: Probability, 2015Co-Authors: Sigrid Kallblad, Xiaolu Tan, Nizar TouziAbstract:We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval $[0,1]$. The problem is related to the study of extremal Martingales associated with a peacock ("process increasing in convex order", by Hirsch, Profeta, Roynette and Yor). A general duality result is obtained by convergence techniques. We then study the case where the reward function depends on the maximum of the embedding process, which is the limit of the Martingale transport problem studied in Henry-Labordere, Obloj, Spoida and Touzi. Under technical conditions, some explicit characteristics of the solutions to the optimal SEP as well as to its dual problem are obtained. We also discuss the associated Martingale inequality.
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Martingale representation theorem for the g expectation
Stochastic Processes and their Applications, 2011Co-Authors: Mete H Soner, Nizar Touzi, Jianfeng ZhangAbstract:This paper considers the nonlinear theory of G-Martingales as introduced by Peng (2007) in [16,17]. A Martingale representation theorem for this theory is proved by using the techniques and the results established in Soner et al. (2009) [20] for the second-order stochastic target problems and the second-order backward stochastic differential equations. In particular, this representation provides a hedging strategy in a market with an uncertain volatility.
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Martingale representation theorem for the g expectation
Social Science Research Network, 2010Co-Authors: Halil Mete Soner, Nizar Touzi, Jianfeng ZhangAbstract:This paper considers the nonlinear theory of G-Martingales as introduced by Peng in [16, 17]. A Martingale representation theorem for this theory is proved by using the techniques and the results established in [20] for the second order stochastic target problems and the second order backward stochastic differential equations. In particular, this representation provides a hedging strategy in a market with an uncertain volatility.
Chuanzhou Zhang - One of the best experts on this subject based on the ideXlab platform.
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atomic decompositions of banach lattice valued Martingales
Statistics & Probability Letters, 2012Co-Authors: Xueying Zhang, Chuanzhou ZhangAbstract:In this paper, atomic decompositions of Banach lattice-valued Martingales are given. We discuss the relation between the LERMT property and atomic decompositions. With the help of atomic decompositions, the relation of the Martingale spaces is investigated.
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atomic decompositions of banach lattice valued Martingales with weighted measure
Scientia Sinica Mathematica, 2012Co-Authors: Chuanzhou Zhang, Xueying ZhangAbstract:In this paper the atomic decompositions of Banach lattice-valued Martingales with weighted measure are given. With the help of the atomic decompositions, the interpolation theorems on Martingale spaces are investigated.
Peter Auer - One of the best experts on this subject based on the ideXlab platform.
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pac bayesian inequalities for Martingales
IEEE Transactions on Information Theory, 2012Co-Authors: Yevgeny Seldin, Francois Laviolette, Nicolo Cesabianchi, John Shawetaylor, Peter AuerAbstract:We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent Martingales. Our results extend the PAC-Bayesian (probably approximately correct) analysis in learning theory from the i.i.d. setting to Martingales opening the way for its application to importance weighted sampling, reinforcement learning, and other interactive learning domains, as well as many other domains in probability theory and statistics, where Martingales are encountered. We also present a comparison inequality that bounds the expectation of a convex function of a Martingale difference sequence shifted to the [0, 1] interval by the expectation of the same function of independent Bernoulli random variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma's inequality.
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pac bayesian inequalities for Martingales
Uncertainty in Artificial Intelligence, 2012Co-Authors: Yevgeny Seldin, Francois Laviolette, Nicolo Cesabianchi, John Shawetaylor, Peter AuerAbstract:We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent Martingales. Our results extend the PAC-Bayesian analysis in learning theory from the i.i.d. setting to Martingales opening the way for its application in reinforcement learning and other interactive learning domains, as well as many other domains in probability theory and statistics, where Martingales are encountered. We also present a comparison inequality that bounds the expectation of a convex function of a Martingale difference sequence shifted to the [0,1] interval by the expectation of the same function of independent Bernoulli variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma's inequality. For the complete paper see Seldin et al. (2012).
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pac bayesian inequalities for Martingales
arXiv: Learning, 2011Co-Authors: Yevgeny Seldin, Francois Laviolette, Nicolo Cesabianchi, John Shawetaylor, Peter AuerAbstract:We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent Martingales. Our results extend the PAC-Bayesian analysis in learning theory from the i.i.d. setting to Martingales opening the way for its application to importance weighted sampling, reinforcement learning, and other interactive learning domains, as well as many other domains in probability theory and statistics, where Martingales are encountered. We also present a comparison inequality that bounds the expectation of a convex function of a Martingale difference sequence shifted to the [0,1] interval by the expectation of the same function of independent Bernoulli variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma's inequality.
Sigrid Kallblad - One of the best experts on this subject based on the ideXlab platform.
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optimal skorokhod embedding given full marginals and azema yor peacocks
Annals of Applied Probability, 2017Co-Authors: Sigrid Kallblad, Xiaolu Tan, Nizar TouziAbstract:We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval $[0,1]$. The problem is related to the study of extremal Martingales associated with a peacock (“process increasing in convex order,” by Hirsch, Profeta, Roynette and Yor [Peacocks and Associated Martingales, with Explicit Constructions (2011), Springer, Milan]). A general duality result is obtained by convergence techniques. We then study the case where the reward function depends on the maximum of the embedding process, which is the limit of the Martingale transport problem studied in Henry-Labordere, Obloj, Spoida and Touzi [Ann. Appl. Probab. 26 (2016) 1–44]. Under technical conditions, we then characterize the optimal value and the solution to the dual problem. In particular, the optimal embedding corresponds to the Madan and Yor [Bernoulli 8 (2002) 509–536] peacock under their “increasing mean residual value” condition. We also discuss the associated Martingale inequality.
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optimal skorokhod embedding given full marginals and azema yor peacocks
arXiv: Probability, 2015Co-Authors: Sigrid Kallblad, Xiaolu Tan, Nizar TouziAbstract:We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval $[0,1]$. The problem is related to the study of extremal Martingales associated with a peacock ("process increasing in convex order", by Hirsch, Profeta, Roynette and Yor). A general duality result is obtained by convergence techniques. We then study the case where the reward function depends on the maximum of the embedding process, which is the limit of the Martingale transport problem studied in Henry-Labordere, Obloj, Spoida and Touzi. Under technical conditions, some explicit characteristics of the solutions to the optimal SEP as well as to its dual problem are obtained. We also discuss the associated Martingale inequality.
