Constructing sublinear expectations on path space
Marcel Nutz,Ramon van Handel +1 more
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TLDR
In this paper, a general construction of time-consistent sublinear expectations on the space of continuous paths is provided, which yields the existence of the conditional G -expectation of a Borel-measurable (rather than quasi-continuous) random variable, and an optional sampling theorem that holds without exceptional set.About:
This article is published in Stochastic Processes and their Applications.The article was published on 2013-08-01 and is currently open access. It has received 163 citations till now. The article focuses on the topics: Sublinear function & Nonlinear expectation.read more
Citations
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Arbitrage and Duality in Nondominated Discrete-Time Models
Bruno Bouchard,Marcel Nutz +1 more
TL;DR: In this article, the authors consider a non-nominated model of a discrete-time financial market where stocks are traded dynamically and options are available for static hedging, and show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of martingale measures.
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A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options
TL;DR: This work provides a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem, and shows that this formulation allows to recover previously known results about Lookback options.
Journal ArticleDOI
Superreplication under Volatility Uncertainty for Measurable Claims
Ariel Neufeld,Marcel Nutz +1 more
TL;DR: In this paper, the duality-formula for the superreplication price in a setting of volatility uncertainty was established, including the example of random $G$-expectation, and the contingent claim was not assumed to be quasi-continuous.
Journal ArticleDOI
Nonlinear Lévy Processes and their Characteristics
Ariel Neufeld,Marcel Nutz +1 more
TL;DR: In this article, the authors developed a general construction for nonlinear Levy processes with given characteristics, and constructed a sublinear expectation on Skorohod space under which the canonical process has stationary independent increments and a nonlinear generator corresponding to the supremum of all generators of all classical Levy process with triplets.
References
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Multidimensional Diffusion Processes
TL;DR: In this paper, the authors propose extension theorems, Martingales, and Compactness, as well as the non-unique case of the Martingale problem, and some estimates on the transition probability functions.
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Stochastic Finance: An Introduction in Discrete Time
Hans Föllmer,Alexander Schied +1 more
TL;DR: In this article, the authors present an introduction to financial mathematics, focusing on stochastic models in discrete time, with a focus on the problem of pricing and hedging of financial derivatives.
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Stochastic optimal control : the discrete time case
TL;DR: This research monograph is the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including thetreatment of the intricate measure-theoretic issues.
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G -Expectation, G -Brownian Motion and Related Stochastic Calculus of Itô Type
TL;DR: In this article, the authors introduce a nonlinear expectation generated by a heat equation with infinitesimal generator G. The G-standard normal distribution is introduced and the canonical process is a G-Brownian motion.
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