Strassen's theorem for biased convex order

2025/09/16 by Acciaio, Beatrice, Beiglböck, Mathias, Kolosov, Evgeny +1
#49Q22 #60E15 #60G42 #91G20 #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.13041

Abstract

Strassen's theorem asserts that for given marginal probabilities μ,ν there exists a martingale starting in μ and terminating in ν if and only if μ,ν are in convex order. From a financial perspective, it guarantees the existence of market-consistent martingale pricing measures for arbitrage-free prices of European call options and thus plays a fundamental role in robust finance. Arbitrage-free prices of American options demand a stronger version of martingales which are 'biased' in a specific sense. In this paper, we derive an extension of Strassen's theorem that links them to an appropriate strengthening of the convex order. Moreover, we provide a characterization of this order through integrals with respect to compensated Poisson processes.

Citations

• Calibration of the Bass Local Volatility model
• An optimal transport based characterization of convex order
• Existence, Duality, and Cyclical monotonicity for weak transport costs
• Martingale Benamou--Brenier: a probabilistic perspective
• Optimal Transport and Skorokhod Embedding
• A model-free version of the fundamental theorem of asset pricing and the\n super-replication theorem
• Prices of State-Contingent Claims Implicit in Option Prices

Related

• On Strassen's Theorem for support functions
• Convex order for path-dependent derivatives: a dynamic programming approach
• Applications of Strassen's theorem and Choquet theory to optimal transport problems, to uniformly convex functions and to uniformly smooth functions
• Approximation of martingale couplings on the line in the weak adapted topology
• Convex Order and Arbitrage