Scaling Limits for Exponential Hedging in the Brownian Framework

Paper: arXiv 2502.17186

Authors: Yan Dolinksy, Xin Zhang

Abstract

In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the \emph{specific relative entropy}, and in addition we construct asymptotic optimal hedging strategies. To prove the upper bound for the limit, we formulate the dual problem as a stochastic control, and show there exists a classical solution to its Hamilton-Jacobi-Bellman (HJB) equation. The proof for the lower bound relies on the duality result for exponential hedging in discrete time.

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 rigorous mathematical proofs involving HJB equations, stochastic control, and specific relative entropy to establish scaling limits for exponential utility indifference pricing. However, it is purely theoretical and lacks empirical evaluation or backtesting on real-world market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Compute scaling limits of exponential indifference prices in Bachelier model] --> B[Inputs: European claims & Brownian framework]
    B --> C[Methodology: Upper & Lower Bound Analysis]
    
    C --> D[Upper Bound: Formulate dual stochastic control & solve HJB equation]
    C --> E[Lower Bound: Apply duality results from discrete-time exponential hedging]
    
    D --> F[Key Outcome: Scaling limit represented via Specific Relative Entropy]
    E --> F
    F --> G[Practical Result: Construction of asymptotic optimal hedging strategies]