Paper: arXiv 2401.05713

Authors: Tahir Choulli, Emmanuel Lepinette

Abstract

In this paper, we consider the discrete-time setting, and the market model described by (S,F,T)$. Herein F is the ``public" flow of information which is available to all agents overtime, S is the discounted price process of d-tradable assets, and T is an arbitrary random time whose occurrence might not be observable via F. Thus, we consider the larger flow G which incorporates F and makes T an observable random time. This framework covers the credit risk theory setting, the life insurance setting and the setting of employee stock option valuation. For the stopped model (S^T,G) and for various vulnerable claims, based on this model, we address the super-hedging pricing valuation problem and its intrinsic Immediate-Profit arbitrage (IP hereafter for short). Our first main contribution lies in singling out the impact of change of prior and/or information on conditional essential supremum, which is a vital tool in super-hedging pricing. The second main contribution consists of describing as explicit as possible how the set of super-hedging prices expands under the stochasticity of T and its risks, and we address the IP arbitrage for (S^T,G) as well. The third main contribution resides in elaborating as explicit as possible pricing formulas for vulnerable claims, and singling out the various informational risks in the prices’ dynamics.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using filtration expansion and conditional essential supremum to address super-hedging under random horizons. While mathematically sophisticated and novel in its handling of informational risks, it lacks empirical validation or numerical implementation.

Research Flowchart

  flowchart TD
    A[Research Goal: Super-hedging Pricing & IP Arbitrage under Random Horizon T] --> B[Inputs: Market Model S, Public Info F, Random Time T]
    B --> C[Expand Information Flow: Upgrade F to G to make T observable]
    C --> D[Methodology: Analyze impact of Info/Prior changes on Conditional Essential Supremum]
    D --> E[Computational Step: Evaluate Stopped Model S^T & Derive Vulnerable Claim Formulas]
    E --> F[Outcomes: Explicit Pricing Formulas, IP Arbitrage Conditions & Info Risk Dynamics]