Paper: arXiv 2408.13048

Authors: Shuzhen Yang, Wenqing Zhang

Abstract

In this study, we consider the asset pricing under model uncertainty with discrete time and states structure. For the single-period securities model, we give a novel definition of arbitrage under a family of probability, and explore of its relationship with risk neutral probability measure. Focusing on the financial market with short sales prohibitions, we separately investigate the necessary and sufficient conditions for no-arbitrage asset pricing based on nonlinear expectation which composed with a family of probability. When each linear expectation driven by the probability in the family of probability becomes a martingale measure, the necessary and sufficient conditions are same, which coincide with the existing results. Furthermore, we expand the main results of single-period securities model to the case of multi-period securities model. By-product, we obtain the superhedging prices of contingent claim under model uncertainty.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical treatment extending the Fundamental Theorem of Asset Pricing and superhedging under Knightian uncertainty with short-sale constraints using sublinear expectations. However, it is purely theoretical with no empirical backtesting, real market data application, or numerical simulation.

Research Flowchart

  flowchart TD
    A["Research Goal: Asset Pricing & Arbitrage<br>under Model Uncertainty (Discrete Time/States)"] --> B["Inputs: Securities Market Model<br>+ Short Sales Prohibitions<br>+ Set of Probability Measures"]
    B --> C["Single-Period Model Analysis:<br>Define Arbitrage under Ambiguity &<br>Apply Nonlinear Expectation"]
    C --> D["Multi-Period Extension &<br>Martingale Measure Conditions"]
    D --> E["Key Outcomes:<br>1. Necessary & Sufficient No-Arbitrage Conditions<br>2. Coincidence with classic results under Martingales<br>3. Superhedging Prices for Contingent Claims"]