G -forward performance process and representation of homothetic case via ergodic quadratic G -BSDE

Abstract

We introduce a new type of robust forward criterion under model uncertainty, called the G -forward performance process, which extends the classical notion of forward performance process to the G -expectation framework. We then derive the representations of homothetic G -forward performance processes in a single stochastic factor model with uncertainty, building on the well-posedness of ergodic and infinite horizon backward stochastic differential equations driven by G -Brownian motion (G -BSDEs) with quadratic generators.

Keywords

G -forward performance process / Infinite horizon G -BSDE / Ergodic G -BSDE

Acknowledgements

The authors would like to thank the editor and the anonymous referee for their valuable suggestions and comments. The research of Falei Wang is supported by the National Natural Science Foundation of China (Grant Nos. 12171280 and 12031009), the Natural Science Foundation of Shandong Province (Grant Nos. ZR2021YQ01 and ZR2022JQ01) and the National Key Research & Development Program of China (Grant No. 2018YFA0703900).

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