Paper: arXiv 2408.02137

Authors: Fabrice Baudoin, Oleksii Mostovyi

Abstract

We propose indifference pricing to estimate the value of the weak information. Our framework allows for tractability, quantifying the amount of additional information, and permits the description of the smallness and the stability with respect to small perturbations of the weak information. We provide sharp conditions for the stability with counterexamples. The results rely on a theorem of independent interest on the stability of the optimal investment problem with respect to small changes in the physical probability measure. We also investigate contingent claims that are indifference price invariant with respect to changes in weak information. We show that, in incomplete models, the class of information-invariant claims includes the replicable claims, and it can be strictly bigger. In particular, in complete models, all contingent claims are information invariant. We augment the results with examples and counterexamples.

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 framework for analyzing the value of weak information using indifference pricing and stochastic control theory. While mathematically sophisticated with solid theoretical completeness and sharp stability proofs, it lacks empirical backtesting or real-world financial data applications.

Research Flowchart

  flowchart TD
    A[Goal: Value & Analyze Weak Information via Indifference Pricing] --> B[Input: Market Model & Utility Functions]
    B --> C[Method: Formulate Optimal Investment Problem under Measure Perturbations]
    C --> D[Prove Theorem: Stability of Utility Maximization vs Physical Measure Changes]
    D --> E[Derive Sharp Conditions for Information Stability & Identify Counterexamples]
    D --> F[Analyze Information-Invariant Contingent Claims]
    
    E & F --> G[Outcomes: Quantified Info Value, Stability Bounds & Proof that Invariant Claims Include Replicable Claims]