Martingale Theory for Dynkin Games with Asymmetric Information

Battle Count: 79

The paper has moderate relevance to quantitative trading. It provides theoretical foundations for game options (Kifer 2000), optimal stopping with asymmetric information relevant to regime-switching trading strategies, and war-of-attrition models applicable to strategic execution. The partially observed dynamics framework (Section 5.2) with diffusion processes and belief updating is directly relevant to trading under uncertainty about market regimes. However, the paper is primarily theoretical and does not provide implementable trading strategies or backtesting results. The connection to financial applications is through the mathematical framework rather than direct trading algorithms.

Extremely high complexity. The paper develops a fully general non-Markovian martingale theory for stochastic games with arbitrary information structures. Implementation would require: (1) working with optional semimartingales and their Doob-Meyer decompositions; (2) handling randomised stopping times via generating processes; (3) computing optional projections under asymmetric filtrations; (4) solving variational inequalities or PDE systems for specific Markovian instances; (5) managing belief processes and dynamic changes of measure. The theoretical framework is highly abstract, and concrete implementation requires significant additional work for specific game classes.

The paper is purely theoretical with complete mathematical proofs. All definitions, theorems, propositions, lemmas, and corollaries are rigorously stated and proved. The framework is self-contained with detailed appendices covering aggregation results, directed families, and technical lemmas. However, the extreme generality (non-Markovian, arbitrary information structures) makes direct numerical reproduction of specific examples challenging without additional computational tools.