Semistatic robust utility indifference valuation and robust integral functionals

Paper: arXiv 2402.18872

Authors: Keita Owari

Abstract

We consider a discrete-time robust utility maximisation with semistatic strategies, and the associated indifference prices of exotic options. For this purpose, we introduce a robust form of convex integral functionals on the space of bounded continuous functions on a Polish space, and establish some key regularity and representation results, in the spirit of the classical Rockafellar theorem, in terms of the duality formed with the space of Borel measures. These results (together with the standard Fenchel duality and minimax theorems) yield a duality for the robust utility maximisation problem as well as a representation of associated indifference prices, where the presence of static positions in the primal problem appears in the dual problem as a marginal constraint on the martingale measures. Consequently, the resulting indifference prices are consistent with the observed prices of vanilla options.

Complexity vs Empirical Score

• Math Complexity: 9.2/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a deeply rigorous theoretical framework using advanced functional analysis, Rockafellar-type duality, and robust optimization for utility indifference pricing. However, it is entirely mathematical and lacks empirical backtesting, real-world data application, or executable code.

Research Flowchart

  flowchart TD
    A[Research Goal: Robust Utility Indifference Valuation with Semistatic Strategies] --> B[Inputs: Exotic Options & Observed Vanilla Option Prices]
    B --> C[Methodology: Introduce Robust Convex Integral Functionals on Polish Space]
    C --> D[Apply Rockafellar Theorem, Fenchel Duality & Minimax Theorems]
    D --> E[Dual Problem Formulation: Martingale Measures with Marginal Constraints]
    E --> F[Outcomes: Robust Utility Maximisation Duality & Consistency with Vanilla Prices]