Superreplication under Volatility Uncertainty for Measurable Claims

By Ariel Neufeld, Marcel Nutz. 2012

101 citations recorded by the source corpus.

We establish the duality-formula for the superreplication price in a setting of volatility uncertainty which includes the example of "random $G$-expectation". In contrast to previous results, the contingent claim is not assumed to be quasi-continuous.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/e3d8116baaf52502ece4a89b7ff20d6b8bb3fbd4

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Citations in the corpus

The maximum maximum of a martingale with given $\mathbf{n}$ marginals (2012, background): “More recently, Neufeld and Nutz [30] relaxed the uniform continuity condition, allowing for a larger class of random variables including measurable ones.”
Stochastic control for a class of nonlinear kernels and applications (2015, unknown): “, the financial market is complete under any of the measures considered) this super-hedging price has been thoroughly studied in the recent literature; see among others [2, 7, 26, 27, 65, 70, 72, 76, 78, 83, 85, 86].”
Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems (2013, methodology): “Using similar ideas, but in a non-Markovian context and with a more modern presentation, Nutz and van Handel (2013, [36]), Neufeld and Nutz (2013, [34]) and Zitkovic (2014, [48]) provided the DPP for a class of control problems by considering their law on the canonical space of paths.”
Capacities, Measurable Selection and Dynamic Programming Part I: Abstract Framework (2013, background): “In the same spirit, Nutz and van Handel [27] proposed a general construction of time-consistence sublinear expectations on the canonical space, where their time-consistence property is a reformulation of the DPP.”
UTILITY MAXIMIZATION UNDER MODEL UNCERTAINTY IN DISCRETE TIME (2013, background): “The robust superhedging problem has been studied in several settings; see [1, 4, 6, 11, 13, 17, 23, 26, 32, 33], among others.”
Complete Duality for Martingale Optimal Transport on the Line (2015, background): “, [1, 8, 13, 14, 15, 16, 22, 35] for models in discrete time and [6, 11, 18, 17, 20, 21, 24, 25, 32, 34, 36, 38, 40] for continuous-time models.”
Nonlinear Lévy Processes and their Characteristics (2016, background): “Keywords Nonlinear Lévy process; Sublinear expectation; Partial integro-differential equation; Semimartingale characteristics; Knightian uncertainty AMS 2010 Subject Classification 60G51; 60G44; 93E20”
Measurability of semimartingale characteristics with respect to the probability law (2013, background): “Other examples where sets of semimartingale laws play a role are path-dependent PDEs [10], robust superhedging as in [16, 25] or nonlinear optimal stopping problems as in [21], to name but a few.”
On the Robust superhedging of measurable claims (2013, unknown): “Therefore, we need to extend the results of [9] in order to address the case of Pm.”
Arbitrage and duality in nondominated discrete-time models (2013, background): “In the setting where no options are traded and P is supposed to consist of martingale measures in the rst place, there is a substantial literature on superhedging under volatility uncertainty, where S is a (continuous-time) process with continuous trajectories; see, among others, [8, 27, 40, 41, 42,”
ROBUST FUNDAMENTAL THEOREM FOR CONTINUOUS PROCESSES (2014, background): “[5, 16, 20, 30, 36, 38, 39, 41, 44, 45], among others, or when all paths are considered possible for the stock and options are also traded; see, e.”
McKean–Vlasov optimal control: The dynamic programming principle (2019, result): “Similar results were obtained by several authors, among which we mention Nutz and Soner [63], Neufeld and Nutz [61; 62], Nutz and van Handel [64], Žitković [82], and Possamaï, Tan, and Zhou [68].”
Optimal stopping under adverse nonlinear expectation and related games (2012, background): “Moreover, as Xτ∗ is Borelmeasurable and bounded, the (European) superhedging result stated in [23], Theorem 2.”