An ordinary differential equation for entropic optimal transport and its linearly constrained variants

We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two marginal problems, applies to multi-marginal problems and those with additional linear constraints. Solving the ODE gives a new numerical method to solve the optimal transport problem, which has the advantage of yielding the solution for all intermediate values of the ODE parameter (which is equivalent to the usual regularization parameter). We illustrate this method with several numerical simulations. The formulation of the ODE also allows one to compute derivatives of the optimal cost when the ODE parameter is $0$, corresponding to the fully regularized limit problem in which only the entropy is minimized.Comment: 38 pages, 6 figures, 5 table

Geometry of vectorial martingale optimal transport and robust option pricing

This paper addresses robust finance, which is concerned with the development of models and approaches that account for market uncertainties. Specifically, we investigate the Vectorial Martingale Optimal Transport (VMOT) problem, the geometry of its solutions, and its application with robust option pricing problems in finance. To this end, we consider two-period market models and show that when the spatial dimension $d$ (the number of underlying assets) is 2, the extremal model for the cap option with a sub- or super-modular payout reduces to a single factor model in the first period, but not in general when $d > 2$. The result demonstrates a subtle relationship between spatial dimension, cost function supermodularity, and their effect on the geometry of solutions to the VMOT problem. We investigate applications of the model to financial problems and demonstrate how the dimensional reduction caused by monotonicity can be used to improve existing computational methods

BERT-based Financial Sentiment Index and LSTM-based Stock Return Predictability

Traditional sentiment construction in finance relies heavily on the dictionary-based approach, with a few exceptions using simple machine learning techniques such as Naive Bayes classifier. While the current literature has not yet invoked the rapid advancement in the natural language processing, we construct in this research a textual-based sentiment index using a novel model BERT recently developed by Google, especially for three actively trading individual stocks in Hong Kong market with hot discussion on Weibo.com. On the one hand, we demonstrate a significant enhancement of applying BERT in sentiment analysis when compared with existing models. On the other hand, by combining with the other two existing methods commonly used on building the sentiment index in the financial literature, i.e., option-implied and market-implied approaches, we propose a more general and comprehensive framework for financial sentiment analysis, and further provide convincing outcomes for the predictability of individual stock return for the above three stocks using LSTM (with a feature of a nonlinear mapping), in contrast to the dominating econometric methods in sentiment influence analysis that are all of a nature of linear regression.Comment: 10 pages, 1 figure, 5 tables, submitted to NeurIPS 2019, under revie