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, this result guarantees the existence of arbitrage-free models consistent with observed prices of European options and thus plays a fundamental role in robust finance. We show that existence of arbitrage-free models consistent with observed prices of American options requires a stronger version of martingales which are ‘biased’ in a specific sense. For this, we derive an extension of Strassen’s theorem which links them to an appropriate strengthening of the convex order, and provide an integral characterization of the latter. Based on joint work with M. Beiglboeck, E. Kolosov, G. Pammer.

Bio: Beatrice Acciaio is Professor of Mathematics at the Swiss Federal Institute of Technology (ETH) Zurich since 2020. Before joining ETH, she was associate professor at the London School of Economics, and prior to that she has held positions at the University of Vienna and at the University of Perugia. Beatrice obtained her PhD in Applied Mathematics from the University of Perugia under the supervision of Walter Schachermayer.

Her primary research interests are in stochastic analysis and optimal transports, and their applications in finance, insurance and economics, in particular concerning robust approaches to finance and decision-making under uncertainty.

Beatrice is executive secretary of the Bachelier Finance Society, and Associate Editor for the SIAM Journal on Financial Mathematics, Finance and Stochastics, Mathematical Finance, Annals of Applied Probability, International Journal of Theoretical and Applied Finance, and the Bocconi & Springer Series on Mathematics, Statistics, Finance and Economics.

Beatrice was awarded the 2022 Louis Bachelier prize for her contributions to financial mathematics.