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Learn the fundamentals of adapted optimal transport theory and explore its practical applications in this mathematical lecture delivered by Mathias Beiglboeck from the University of Vienna at the Fields Institute. Discover how adapted optimal transport extends classical optimal transport theory by incorporating filtration structures and temporal constraints, making it particularly relevant for financial mathematics and stochastic processes. Examine the theoretical foundations that bridge optimal transport with martingale theory and understand how these concepts apply to model-independent pricing in mathematical finance. Explore key techniques for constructing optimal couplings under adapted constraints and investigate how these methods solve problems in robust hedging and arbitrage theory. Gain insights into the geometric and probabilistic aspects of adapted transport plans and their role in understanding the structure of martingale measures. Study concrete examples that illustrate the differences between classical and adapted optimal transport, including applications to exotic option pricing and risk management. Understand the computational challenges and numerical approaches used to solve adapted optimal transport problems in practice.
