Backward Nonlinear Expectation Equations

Mathematics and Financial Economics, Vol. 12, No. 1, pp. 111-134, 2018

Posted: 11 Jan 2015 Last revised: 10 Jan 2019

See all articles by Christoph Belak

Christoph Belak

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften

Thomas Seiferling

University of Kaiserslautern - Department of Mathematics

Frank Thomas Seifried

University of Trier

Date Written: August 1, 2017

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. 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

JEL Classification: D81, D91

Suggested Citation

Belak, Christoph and Seiferling, Thomas and Seifried, Frank Thomas, Backward Nonlinear Expectation Equations (August 1, 2017). Mathematics and Financial Economics, Vol. 12, No. 1, pp. 111-134, 2018, Available at SSRN: https://ssrn.com/abstract=2547940 or http://dx.doi.org/10.2139/ssrn.2547940

Christoph Belak (Contact Author)

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften ( email )

Institut fur Mathematik, Sekr. MA 7-1
Strasse des 17. Juni 136
Berlin, 10623
Germany

Thomas Seiferling

University of Kaiserslautern - Department of Mathematics ( email )

D-67653 Kaiserslautern
Germany

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

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