Paper: arXiv 2603.28256

Authors: Yukihiro Tsuzuki

Abstract

We study the upper hedging price for contingent claims in market models with strong types of arbitrage: increasing profit, strong arbitrage, and arbitrage of the first kind. The existence of arbitrage may make the price smaller than if it did not exist. For example, when the asset price process has a reflecting boundary, which introduces increasing profit in the market model, the option prices are reduced to those of the corresponding options that knock-out at the boundary. Furthermore, we demonstrate that corporate stock price processes with increasing profit are obtained as a result of corporate stock issuance and repurchase plans.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous mathematical treatment of contingent claim valuation under non-standard arbitrage conditions (e.g., strong arbitrage, reflecting boundaries). However, it is purely theoretical with minimal empirical backtesting or data validation, placing it firmly in the theoretical domain.

Research Flowchart

  flowchart TD
    A["Research Question:<br>Impact of strong arbitrage on upper hedging prices"] --> B["Input Assumptions:<br>Market models with Increasing Profit (IP) & Arbitrage 1st Kind"]
    B --> C["Methodology:<br>Superhedging & valuation under reflecting boundary constraints"]
    C --> D["Application:<br>Model corporate stock issuance and repurchase plans"]
    D --> E["Key Outcome 1:<br>Arbitrage reduces upper hedging prices (cheaper options)"]
    D --> F["Key Outcome 2:<br>Reflecting boundaries reduce option values to knock-out options"]