Backward nonlinear expectation equations

Christoph Belak; Thomas Seiferling; Frank Thomas Seifried

doi:10.1007/s11579-017-0199-7

Backward nonlinear expectation equations

Christoph Belak
, Thomas Seiferling
, Frank Thomas Seifried

University of Trier
University of Kaiserslautern

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

1 Scopus citations

Abstract

Building on an abstract framework for dynamic nonlinear expectations that comprises g-, G- and random G-expectations, we develop a theory of backward nonlinear expectation equations of the form Xt=Et[∫tTg(s,X)μ(ds)+ξ],t∈[0,T].We provide existence, uniqueness, and stability results and establish convergence of the associated discrete-time nonlinear aggregations. As an application, we construct continuous-time recursive utilities under ambiguity and identify the corresponding utility processes as limits of discrete-time recursive utilities.

Original language	English
Pages (from-to)	111-134
Number of pages	24
Journal	Mathematics and Financial Economics
Volume	12
Issue number	1
DOIs	https://doi.org/10.1007/s11579-017-0199-7
State	Published - 1 Jan 2018
Externally published	Yes

Keywords

Backward stochastic differential equation
Nonlinear expectation
Random G-expectation
Recursive utility
Volatility uncertainty

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10.1007/s11579-017-0199-7

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abstract = "Building on an abstract framework for dynamic nonlinear expectations that comprises g-, G- and random G-expectations, we develop a theory of backward nonlinear expectation equations of the form Xt=Et[∫tTg(s,X)μ(ds)+ξ],t∈[0,T].We provide existence, uniqueness, and stability results and establish convergence of the associated discrete-time nonlinear aggregations. As an application, we construct continuous-time recursive utilities under ambiguity and identify the corresponding utility processes as limits of discrete-time recursive utilities.",

keywords = "Backward stochastic differential equation, Nonlinear expectation, Random G-expectation, Recursive utility, Volatility uncertainty",

author = "Christoph Belak and Thomas Seiferling and Seifried, \{Frank Thomas\}",

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AU - Seifried, Frank Thomas

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N2 - Building on an abstract framework for dynamic nonlinear expectations that comprises g-, G- and random G-expectations, we develop a theory of backward nonlinear expectation equations of the form Xt=Et[∫tTg(s,X)μ(ds)+ξ],t∈[0,T].We provide existence, uniqueness, and stability results and establish convergence of the associated discrete-time nonlinear aggregations. As an application, we construct continuous-time recursive utilities under ambiguity and identify the corresponding utility processes as limits of discrete-time recursive utilities.

AB - Building on an abstract framework for dynamic nonlinear expectations that comprises g-, G- and random G-expectations, we develop a theory of backward nonlinear expectation equations of the form Xt=Et[∫tTg(s,X)μ(ds)+ξ],t∈[0,T].We provide existence, uniqueness, and stability results and establish convergence of the associated discrete-time nonlinear aggregations. As an application, we construct continuous-time recursive utilities under ambiguity and identify the corresponding utility processes as limits of discrete-time recursive utilities.

KW - Backward stochastic differential equation

KW - Nonlinear expectation

KW - Random G-expectation

KW - Recursive utility

KW - Volatility uncertainty

UR - https://www.scopus.com/pages/publications/85027960299

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SP - 111

EP - 134

JO - Mathematics and Financial Economics

JF - Mathematics and Financial Economics

IS - 1

ER -

Backward nonlinear expectation equations

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Keywords

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