My main research interests are in the area of Backward Stochastic Differential Equations (BSDEs), mathematical modelling of neural networks, probabilistic numerical methods and applications, particularly in financial mathematics.
Some of my contributions include a study of the solution of BSDEs with coefficients or constraints depending on the probability law of the solution (McKean Vlasov BSDEs and mean-reflected BSDEs respectively), the error expansion of the cubature approximation of BSDEs, and its application in the calculation of some financial reserves for Central Counterparties. I have also studied the asymptotic approximation of two-scaled ergodic systems.
I am currently Lecturer at the Department of Mathematics and admissions tutor for the MSc. in Financial Mathematics at UCL . I am Fellow of the Higher Education Academy since 2018. Previously I held a research associate position at University of Nice Sophia Antipolis and UCL. Before starting my academic life, I worked in risk management at FNG.
I completed my undergraduate education in mathematics and in engineering from Universidad de los Andes in Colombia, where I was awarded a Magna cum Laude. An Erasmus Mundus scholar, I obtained my MSc in applied mathematics from University Nice Sophia Antipolis and a Laurea Specialistica from Universita degli Studi dell'Aquila. I completed my PhD studies in applied mathematics at University Nice Sophia Antipolis working under the supervision of François Delarue.
About my last name
My last name is Garcia Trillos. Traditionally in Spanish speaking countries we inherit a composed last name, with one bit belonging to each parent (just as with genes!)