Dr. Mauricio Labadie
Título: Arbitraje estadístico y Backtesting

Resumen de la plática:
En bancos y fondos de inversión, los "quants" (investigadores cuantitativos en Matemáticas Financieras) buscan crear modelos matemáticos para construir estrategias de inversión que sean estadísticamente robustas y redituables. En esta plática hablaremos de qué es un "quant", cuántos tipos de quants hay, qué es el arbitraje estadístico y cuales son sus principios básicos. Terminaremos la charla con un ejemplo de arbitraje estadístico clásico, el "pairs trading", que es una estrategia sistemática de inversión basada el principio de retorno a la media de los precios.

Dr. Fabricio Otoniel Pérez Pérez
Título: "Approximate solutions to an ATI-SAR data inversion problem in oceanography. A continuous Newton’s method approach".

Resumen de la plática:
Over the past four decades, the study of the ocean surface and its dynamics has greatly benefited from the employment of remote-sensing techniques, such as the Synthetic Aperture Radar (SAR). In particular, the ATI-SAR velocity bunching model (ATI-SAR-VB) has the capability to form reliable SAR images of ocean surfaces that exhibit swell patterns. Under the appropriate scenario —where the velocity bunching theory is valid— the main objective of our research is described as follows: "Given the ATI-SAR data D of an unknown scalar field z of sea surface elevations, estimate its associated scalar field ur of radial velocities". Within the context of this inverse problem, the ATI-SAR-VB model is now regarded as a nonlinear integral equation, whose solution is obtained from two different techniques: the solution to a system of nonlinear equations, and the minimisation of a functional. Weapply the Newton's method on function spaces, where the Fréchet derivative of each objective function is analytically calculated. These continuous methods are discretised, in order to produce the corresponding numerical algorithms. The estimated solutions improve upon the solutions that are obtained by the Goldstein-Zebker ATI-SAR principle. On efficiency, the continuous approach is computationally faster than the classical discretise-then-optimise strategy.