One dimensional BSDEs with logarithmic growth application to PDEs

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.

Keywords:

• Backward stochastic differential equations
• viscosity solution
• semilinear PDEs
• logarithmic growth
• logarithmic nonlinearity

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].