Paper: arXiv 2512.21115

Authors: Wenqing Zhang

Abstract

In this study, we investigate asset price bubbles in a discrete-time, discrete-state market under model uncertainty and short sales prohibitions. Building on a new fundamental theorem of asset pricing and a superhedging duality in this setting, we introduce a notion of bubble based on a novel definition of the fundamental price, and analyze their types and characterization. We show that two distinct types of bubbles arise, depending on the maturity structure of the asset. For assets with bounded maturity and no dividend payments, the $G$-supermartingale property of prices provides a necessary and sufficient condition for the existence of bubbles. In contrast, when maturity is unbounded, the infi-supermartingale property yields a necessary condition, while the $G$-supermartingale property remains sufficient. Moreover, there is no bubble under a strengthened no dominance condition. As applications, we examine price bubbles for several standard contingent claims. We show that put-call parity generally fails for fundamental prices, whereas it holds for market prices under no dominance assumption. Furthermore, we establish bounds for the fundamental and market prices of American call options in terms of the corresponding European call prices, adjusted by the associated bubble components.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical exploration of asset price bubbles under model uncertainty and short-sales constraints using advanced sublinear expectation and G-martingale theory. However, it is purely mathematical finance with no empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Question: Asset Price Bubbles<br>under Model Uncertainty & Short-Sale Constraints"] --> B["Inputs: Discrete-time/state Market,<br>Non-linear Expectation (G-expectation),<br>Short-Sales Prohibitions"]
    B --> C["Methodology: Develop New FTAP,<br>Superhedging Duality & Dual Fundamental Price"]
    C --> D["Theoretical Analysis:<br>Characterize Bubble Types by Maturity Structure"]
    D --> E1["Bounded Maturity:<br>Bubble iff G-supermartingale"]
    D --> E2["Unbounded Maturity:<br>G-supermartingale (Sufficient)<br>Infi-supermartingale (Necessary)"]
    D --> E3["Strengthened No-Dominance:<br>No Bubbles Exist"]
    E1 & E2 & E3 --> F["Key Outcomes:<br>• Failure of Put-Call Parity for Fundamental Prices<br>• American vs. European Call Option Bounds via Bubbles"]

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2 of 149 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.