Constructing Sublinear Expectations on Path Space

By Marcel Nutz, Ramon van Handel. 2012

142 citations recorded by the source corpus.

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that holds without exceptional set. Our results also shed light on the inherent limitations to constructing sublinear expectations through aggregation.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ffe20944ad7fce37526622bd9e5445b33cec1d3f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Nonlinear Lévy Processes and their Characteristics (2016, background): “Any element (b, c, F ) ∈ Rd × Sd+ × L is called a Lévy triplet and indeed, there exists a Lévy process having (b, c, F ) as its differential characteristics.”
UTILITY MAXIMIZATION UNDER MODEL UNCERTAINTY IN DISCRETE TIME (2013, unknown): “35 97 v1 [ qfi n. PM ] 1 Keywords Utility maximization; Knightian uncertainty; Nondominated model AMS 2000 Subject Classification 91B28; 93E20; 49L20”
A complete representation theorem for G-martingales (2012, background): “The theory has received very strong attention in the literature in recent years, we refer to the survey paper [20] and the references therein as well as some more recent developments: [4,5,10,12,13,15,16,26], to mention a few.”
Capacities, Measurable Selection and Dynamic Programming Part I: Abstract Framework (2013, methodology): “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.”
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].”
ROBUST FUNDAMENTAL THEOREM FOR CONTINUOUS PROCESSES (2014, methodology): “We impose the following structural conditions—compare with Neufeld and Nutz (2013) and Nutz and van Handel (2013) in the case ζ ≡ ∞.”
Exponential utility maximization under model uncertainty for unbounded endowments (2016, unknown): “is upper semianalytic as a mapping of ω ∈ Ωt whenever X : Ωt+1 → R is, see [8, 34].”
Measurability of semimartingale characteristics with respect to the probability law (2013, unknown): “16 24 v3 [ m at h. PR Keywords Semimartingale characteristics; Semimartingale property; Doob–Meyer decomposition AMS 2010 Subject Classification 60G44; 93E20”
Stochastic control for a class of nonlinear kernels and applications (2015, background): “On the other hand, there is more hope for the probabilistic approach of the 2BSDEs, since, as shown in [65] in the case of linear expectations (that is when the generator of the BSDEs is 0), everything can be well defined by assuming only that the terminal condition is (Borel) measurable.”
Optimal stopping under adverse nonlinear expectation and related games (2012, background): “The Annals of Applied Probability 2015, Vol. 25, No. 5, 2503–2534 DOI: 10.1214/14-AAP1054 © Institute of Mathematical Statistics, 2015”
On the Robust superhedging of measurable claims (2013, unknown): “The same approach is adapted in Galichon, Henry-Labordère and Touzi to obtain the duality result of Theorem 3.1 for uniformly continuous ξ. Recently, Neufeld and Nutz [9] introduced a new approach which avoids the strong regularity condition on ξ.”
Mean–field moral hazard for optimal energy demand response management (2019, methodology): “1 piiiq–pvq] are also satisfied by the set of measures P, see for instance Nutz and van Handel [39].”
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.”
Arbitrage and duality in nondominated discrete-time models (2013, background): “The authors thank Mathias Beiglböck and Jan Obłój for their constructive comments.”