Helder Rojas

Project: Higher-Order Diffusion Theory



Motivated by physical and chemical applications, we are interested in investigating connections between higher order partial differential equations (EDP) and stochastic differential equations (SDE) with imaginary diffusion. In particular, we are interested in extending some existing results in the literature about the study of EDPs, of order 3 or greater, that are unstable in the Hadamard sense, by means of Itô diffusions, subordinated in the complex plane.

Joint work with:
Carlos Escudero Liébana
Department of Fundamental Mathematics-UNED, Spain.




Project: Optimization and Machine Learning for High Frequency Trading Algorithms



The term "algorithmic trading" is used to refer to automatic trading of assets using a predetermined set of decision rules. These rules may be motivated by financial, mathematical, and/or statistical arguments about the assets. Often relevant factors can be identified to operate optimally in the market such as the prices, spread, order flow, market depth and available liquidity in the order book. The objective of this project is to study algorithmic trading problems using optimization and machine learning methods. First we will study how the data behaves, examining the dynamic effects on the prices evolution and factors that determine their dynamics. We will use machine learning methods, to model and classify next direction of price variation, we will use Gaussian Process Models, Functional Data Models and Topological Data Analysis. On the other hand, we will study how to pose optimization problems to mathematically solve certain kinds of problems including efficient allocations, optimal order execution, pairs trading and statistical arbitrage.

Joint work with:
Alberto Ramos
Department of Mathematics-UFPR, Brazil.