Non-linear optimal stopping with Bermudan strategies: the infinite horizon case

Battle Count: 62

The paper is relevant to quantitative trading primarily through its theoretical framework for optimal stopping under non-linear evaluations, which connects to pricing American/Bermudan options in non-linear market models. The g-expectation example from BSDEs is directly applicable to risk-adjusted pricing. However, the paper is purely theoretical with no numerical algorithms, backtesting, or empirical validation, limiting its direct practical applicability. The infinite horizon setting is relevant for perpetual options but less common in typical trading strategies. The Bermudan strategy framework is practically relevant for structured products with discrete exercise dates.

The paper is highly theoretical and abstract, requiring deep expertise in stochastic analysis, optimal stopping theory, BSDEs, and non-linear expectations. There are no algorithms, code, or numerical procedures provided. Implementing the theoretical results would require significant additional work to develop computational methods for the infinite-horizon Bermudan optimal stopping problem under non-linear evaluations. The mathematical framework involves essential suprema over uncountable families of stopping times, non-linear operators with multiple structural properties, and convergence arguments that are non-trivial to discretize.

The paper is a theoretical mathematics paper with complete proofs provided in the main text and appendix. All definitions, assumptions, theorems, and lemmas are rigorously stated and proved. No computational experiments are needed for verification. However, the proofs are highly technical and require deep knowledge of stochastic analysis and optimal stopping theory.