Optimal stopping under G-expectation

Abstract

In this study, we develop a theory of optimal stopping problems within the G-expectation framework. To address this problem, we first introduce a type of random times, called G-stopping times, which are specifically suited for this setting. In the discrete-time case with a finite horizon, we define the value function backward and show that it is the smallest G-supermartingale that dominates the payoff process, ensuring the existence of an optimal stopping time. We then extend these results to both the infinite-horizon case and the continuous-time setting. Moreover, we establish the relationship between the value function and the solution of the reflected backward stochastic differential equation driven by G-Brownian motion.

Keywords

Optimal stopping / G-expectation / G-stopping time / Knightian uncertainty

Acknowledgements

The authors would like to thank the Editor-in-Chief for his attention to the article and appreciate the reviewers for their constructive feedback and valuable suggestions, which have greatly improved the paper.

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