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Financial/Actuarial Mathematics Seminar

Wasserstein metric and its financial applications
Wednesday, January 27, 2021
4:00-5:00 PM Off Campus Location
The talk is concerned with the Wasserstein metric and contains three parts. Motivated by the model-independent pricing of exotic options that is formulated in terms of the martingale optimal transport, we provide in the first part a computational method as well as its convergence rate using the Wasserstein metric. In the second part, we consider an optimization problem originating from an optimal urban planning problem, where the objective function is given by a parameterized semi-discrete Wasserstein distance. It appears that this optimization problem shares the common formulatation with the so-called Wasserstein GAN (Generative Adversarial Network). In contrast to the gradient methods, we adopt Lloyd's algorithm to solve this optimization problem and investigate its convergence. The last part is based on a recent work that is related to two variants: sliced Wasserstein metric and max-sliced Wasserstein metric. We prove that the max-sliced Wasserstein metric (of order 1) is strongly equivalent to the Wasserstein metric, while the sliced Wasserstein metric does not share this nice property. Speaker(s): Gaoyue Guo (UM)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics