Strassen's theorem for biased convex order

Beatrice Acciaio, Mathias Beiglb\"ock, Evgeny Kolosov and Gudmund Pammer

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Abstract: Strassen's theorem asserts that for given marginal probabilities $\mu,\nu$ there exists a martingale starting in $\mu$ and terminating in $\nu$ if and only if $\mu,\nu$ 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.

Date: 2025-09
New Economics Papers: this item is included in nep-inv
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