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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 89, 2017 - Issue 6-7: Proceedings of the Hammamet Conference, 19-23 October 2015
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Articles

One dimensional BSDEs with logarithmic growth application to PDEs

Khaled BahlaliIMATH, EA 2134, UFR Sciences, UTLN, La Garde Cedex, France.View further author information
,
Omar KebiriLaboratory of Statistics and Random Modeling, University of Abou Bekr Belkaid, Tlemcen, Algeria.Correspondence[email protected]
View further author information
,
Nabil KhelfallahLaboratory of Applied Mathematics, University of Mohamed Khider, Biskra, Algeria.View further author information
&
Hadjer MoussaouiIMATH, EA 2134, UFR Sciences, UTLN, La Garde Cedex, France.View further author information
Pages 1061-1081 | Received 12 May 2016, Accepted 21 Mar 2017, Published online: 10 Apr 2017
 
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Abstract

We establish the existence and uniqueness of solutions to one dimensional BSDEs with generator allowing a logarithmic growth () in the state variables y and z. This is done with an integrable terminal value, for some . As byproduct, we obtain the existence of viscosity solutions to PDEs with logarithmic nonlinearities.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Partially supported by PHC Volubilis [MA/10/224]; PHC Tassili [13MDU887].

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