Asset price bubbles under model uncertainty and short-sale constraints: A discrete-time analysis

Battle Count: 114

The paper provides theoretical bounds for American call option prices in terms of European call prices adjusted by bubble components, which could inform options trading strategies. The put-call parity failure for fundamental prices has implications for arbitrage detection. However, the paper is highly theoretical with no empirical validation, making direct implementation challenging. The discrete-time framework is more practical than continuous-time models for algorithmic trading, but the model uncertainty framework requires specifying a family of probability measures, which is non-trivial in practice.

The theoretical framework is mathematically sophisticated, requiring knowledge of sublinear expectations, G-supermartingales, and nonlinear conditional expectations. Implementing the super-hedging duality and computing fundamental prices requires solving optimization problems over families of probability measures. The discrete-state examples are tractable, but scaling to realistic market settings with many states and time periods would be computationally intensive. No code or numerical algorithms are provided.

The paper is purely theoretical with complete mathematical proofs. All definitions, theorems, and proofs are self-contained. However, there are no numerical experiments or code to reproduce. The discrete-state examples (Examples 3.1-3.3) are analytically tractable and can be verified by hand. The framework relies on Peng's sublinear expectation theory and prior work by Yang and Zhang (2024, 2026).