L^p-Solutions and Comparison Results for Lévy Driven BSDEs in a Monotonic, General Growth Setting

Stefan Kremsner; Alexander Steinicke

doi:10.1007/s10959-020-01056-3

L^p-Solutions and Comparison Results for Lévy Driven BSDEs in a Monotonic, General Growth Setting

Stefan Kremsner
, Alexander Steinicke

Lehrstuhl für Angewandte Mathematik (170)

Universität Graz

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Begutachtung

Abstract

We present a unified approach to L ^p-solutions (p> 1) of multidimensional backward stochastic differential equations (BSDEs) driven by Lévy processes and more general filtrations. New existence, uniqueness and comparison results are obtained. The generator functions obey a time-dependent extended monotonicity (Osgood) condition in the y-variable and have general growth in y. Within this setting, the results generalize those of Royer, Yin and Mao, Yao, Kruse and Popier, and Geiss and Steinicke.

Originalsprache	Englisch
Seitenumfang	51
Fachzeitschrift	Journal of theoretical probability
Jahrgang	2020
DOIs	https://doi.org/10.1007/s10959-020-01056-3
Publikationsstatus	Veröffentlicht - 24 Nov. 2020

Bibliographische Notiz

Funding Information:
The authors thank Christel Geiss, University of Jyväskylä, and Gunther Leobacher, University of Graz, for fruitful discussions and valuable suggestions. Stefan Kremsner and Alexander Steinicke are supported by the Austrian Science Fund (FWF): Project F5508-N26, which is part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications.”

Funding Information:
Open access funding provided by Austrian Science Fund (FWF).

Publisher Copyright:
© 2020, The Author(s).

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10.1007/s10959-020-01056-3

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abstract = "We present a unified approach to L p-solutions (p> 1) of multidimensional backward stochastic differential equations (BSDEs) driven by L{\'e}vy processes and more general filtrations. New existence, uniqueness and comparison results are obtained. The generator functions obey a time-dependent extended monotonicity (Osgood) condition in the y-variable and have general growth in y. Within this setting, the results generalize those of Royer, Yin and Mao, Yao, Kruse and Popier, and Geiss and Steinicke. ",

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