Constructing sublinear expectations on path space

Marcel Nutz; Ramon Van Handel

doi:10.1016/j.spa.2013.03.022

Constructing sublinear expectations on path space

Marcel Nutz, Ramon Van Handel

Research output: Contribution to journal › Article › peer-review

77 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	3100-3121
Number of pages	22
Journal	Stochastic Processes and their Applications
Volume	123
Issue number	8
DOIs	https://doi.org/10.1016/j.spa.2013.03.022
State	Published - 2013

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Keywords

Analytic set
Dynamic programming
G-expectation
Optional sampling
Random
Sublinear expectation
Time-consistency

Access to Document

10.1016/j.spa.2013.03.022

Cite this

@article{a9a623be833441c3bc0889de9abb392a,

title = "Constructing sublinear expectations on path space",

abstract = "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.",

keywords = "Analytic set, Dynamic programming, G-expectation, Optional sampling, Random, Sublinear expectation, Time-consistency",

author = "Marcel Nutz and {Van Handel}, Ramon",

note = "Funding Information: The work of R. van Handel is partially supported by the NSF grant DMS-1005575 . Funding Information: The work of M. Nutz is partially supported by the NSF grant DMS-1208985 . ",

year = "2013",

doi = "10.1016/j.spa.2013.03.022",

language = "English (US)",

volume = "123",

pages = "3100--3121",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

number = "8",

}

TY - JOUR

T1 - Constructing sublinear expectations on path space

AU - Nutz, Marcel

AU - Van Handel, Ramon

N1 - Funding Information: The work of R. van Handel is partially supported by the NSF grant DMS-1005575 . Funding Information: The work of M. Nutz is partially supported by the NSF grant DMS-1208985 .

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Analytic set

KW - Dynamic programming

KW - G-expectation

KW - Optional sampling

KW - Random

KW - Sublinear expectation

KW - Time-consistency

UR - http://www.scopus.com/inward/record.url?scp=84877842805&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877842805&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2013.03.022

DO - 10.1016/j.spa.2013.03.022

M3 - Article

AN - SCOPUS:84877842805

SN - 0304-4149

VL - 123

SP - 3100

EP - 3121

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 8

ER -

Constructing sublinear expectations on path space

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this