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Title: On the Restriction of the Optimal Transportation Problem to the set of Martingale Measures with Uniform Marginals
Authors: Saddi, Daryl Allen
Escaner, Jose Maria L. IV
Salazar, Jorge
Keywords: Optimal Transportation
Martingale Measure
Uniform Marginals
Bi-stochastic Matrices
Issue Date: 2019
Publisher: American Institute of Physics Proceedings of The 8th SEAMS-UGM (2019)
Abstract: One of the fundamental problems in mathematical finance is the pricing of derivative assets such as op- tions. In practice, pricing an exotic option, whose value depends on the price evolution of an underlying risky asset, requires a model and then numerical simulations. Having no a priori model for the risky asset, but only the knowledge of its distribution at certain times, we instead look for a lower bound for the option price using the Monge-Kantorovich transportation theory. In this paper, we consider the Monge-Kantorovich problem that is restricted over the set of martingale measure. In order to solve such problem, we first look at sufficient conditions for the existence of an optimal martingale measure. Next, we focus our attention on problems with transports which are two-dimensional real martingale measures with uniform marginals. We then come up with some characterization of the optimizer, using measure-quantization approach.
Type: article
Appears in Collections:MAT - Artigos em Livros de Actas/Proceedings

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