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作者：Herrmann, Sebastian; Stebegg, Florian
作者单位：University of Michigan System; University of Michigan; Columbia University
摘要：We consider the martingale optimal transport duality for cadlag processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semistatic superhedging strategies) are proved for a class of payoffs that includes American, Asian, Bermudan and European options with intermediate maturity. We exhibit an optimal superhedging strategy for which the static part solves an auxiliary problem and the dynamic part is given explicitly in terms of the static part.
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作者：Fukushima, Ryoki; Junk, Stefan
作者单位：Kyoto University; Technical University of Munich
摘要：We study a continuum model of directed polymer in random environment. The law of the polymer is defined as the Brownian motion conditioned to survive among space-time Poissonian disasters. This model is well studied in the positive temperature regime. However, at zero-temperature, even the existence of the free energy has not been proved. In this article, we show that the free energy exists and is continuous at zero-temperature.
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作者：Junnila, Janne; Saksman, Eero; Webb, Christian
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Norwegian University of Science & Technology (NTNU); University of Helsinki; Aalto University
摘要：In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. The first one is a global one and says that if the difference between the covariance kernels of two Gaussian fields, taking values in some Sobolev space, has suitable Sobolev regularity, then these fields differ by a Holder continuous Gaussian ...
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作者：Guo, Gaoyue; Obloj, Jan
作者单位：University of Oxford
摘要：We develop computational methods for solving the martingale optimal transport (MOT) problem-a version of the classical optimal transport with an additional martingale constraint on the transport's dynamics. We prove that a general, multi-step multi-dimensional, MOT problem can be approximated through a sequence of linear programming (LP) problems which result from a discretization of the marginal distributions combined with an appropriate relaxation of the martingale condition. Further, we est...
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作者：Keller-Ressel, Martin; Schmidt, Thorsten; Wardenga, Robert
作者单位：Technische Universitat Dresden; University of Freiburg; University of Freiburg
摘要：In this paper, we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting, times of jumps can be both inaccessible and predictable. To this end, we develop a general theory of finite dimensional affine semimartingales under very weak assumptions. We show that the corresponding semimartingale characteristics have affine form and that the conditional characteristic function can be represented with solutions to measure differential equation...
