Stability and Dual Valuation of Contingent Claims under Rockafellian Perturbations

Battle Count: 57

The paper provides a rigorous theoretical framework for understanding stability of contingent claim pricing and hedging under model perturbations. While not directly producing trading signals or algorithms, it offers important insights for: (1) understanding when pricing models are fragile to small data errors, (2) computing shadow prices that inform hedging decisions, (3) characterizing the value of information in incomplete markets, and (4) identifying conditions under which model-based strategies may fail catastrophically. The connection to the Fundamental Theorem of Asset Pricing and supermartingale measures is directly relevant to quantitative finance practitioners.

The paper is highly theoretical, requiring deep expertise in variational analysis (epi-convergence, hypo-convergence), convex duality, Rockafellian relaxation theory, and stochastic programming. The numerical examples involve constructing scenario trees, solving linear programs, and tracking convergence of dual variables. Implementing the full framework for practical use would require significant mathematical sophistication and custom optimization code. The theoretical results are not directly deployable as a trading system but inform model design and validation.

The paper is primarily theoretical with rigorous proofs. Numerical examples (Sections 6.1 and 6.2) are provided with explicit parameters (Tables 1 and 2) and scenario trees (Figures 3-7), allowing reproduction of the computational illustrations. However, no code repository is provided, and the theoretical framework requires substantial expertise in variational analysis and convex duality to implement.