Felix Kirschner, an ESR at Tilburg University has just completed his online secondment with CNRS-LAAS from April to June 2021.
The purpose of the secondment was to further gather hands-on experience regarding the work in academia. Part of the learnings was to plan and coordinate meetings with a larger group of people and distribute tasks to be worked on. Ultimately, the purpose of the secondment was to produce a piece of research worthy of publication. The people involved were Felix's supervisor Etienne de Klerk as well as Didier Henrion, Milan Korda, Jean-Bernard Lasserre and Victor Magron from CNRS-LAAS.
To initiate the secondment, Felix did a literature review to get understand what methods are the current state of the art to solve problems from Finance, such as options pricing and portfolio optimization. Application of SDP techniques is scarce in the literature, which is why he wanted to start there. Felix and his supervisor proposed a problem of finding optimal bounds on option prices, which can be cast as a generalized moment problem over the non-negative orthant with piecewise affine functions. There are several ways to build a mathematical framework to study this problem and Felix's choice was to study ‘data-driven’ options pricing. Meaning, Felix and the team only rely on available data on options with known prices and do not assume any underlying probability distribution of the asset prices. This framework was also studied by Bertsimas and Popescu [1]. Felix and colleagues aimed to prove convergence of the Lasserre hierarchy for this problem. Felix worked on the software implementation using the Julia language to test the results.
[1] Bertsimas, , Popescu, I. (2002). On the Relation Between Option and Stock Prices: A Convex Optimization Approach. Operations Research. 50.358-374. 10.1287/opre.50.2.358.424.
