Problem
Financial markets can be modeled as large systems of interacting financial agents. These kind of models have been developed in the last twenty years and have raised lots of interest in the past decade. One reason for this is that it seems possible to gain new insights into the origins of market crashes with the help of such models. Another aspect for their popularity is the possibility to model each agent microscopically and still generate macroscopic stock price data with the help of Monte-Carlo simulations.

One challenge in economics is to explain the formation of stylized facts in financial data. Stylized facts are universal market properties, which can be observed at stock markets all over the world. A famous example are Pareto tails in income distributions and stock returns. There is evidence that these stylized facts are a reason for market crashes. Modern financial market models try to reproduce financial data which exhibits stylized facts. Furthermore, there is still an ongoing discussion regarding the connection between behavioral traits of investors and the appearance of stylized facts. Hence, it is crucial to quantify the link between the microscopic model and the macroscopic output. We want to solve this task with the help of uncertainty quantification.

Preliminary work and task
We develop an object oriented C++ framework with several agent based models. Essentially there are several possibilities to work on:

• Compute the influence of several input parameters on the model. We want to use the method algebraic differentiation (AD). Here, one computes the numerical derivative of the model with respect to input parameters. The knowledge of the lecture Computational Differentiation of Prof. Naumann or equivalent qualification is desired.
• Improve the existing C++ framework.
• Implement a GUI or WebApp, not only to run the code with different configurations, but rather analyze the output of the model. This could include statistical errorbars or adaptive routines, which try to quantify the statistical significance of the model output. Depending on the choice of interface, a background in C++ and GUI design using QT or a background in the design of web applications (HTML, JavaScript, AJAX) is required.

Depending on the knowledge and interests of participants the focus can be put on different aspects.

Requirements
As indicated above, different groups need different skills. They are not obligatory but helpful. If you apply for this practical course please state your knowledge in C++, HTML, php, Polymer, WebGL and AD, and please state in which field (AD, modeling/implementation, GUI / web application) you are interested the most. If you already have a favorite partner, please indicate him/her, such that we could select you both during the registration process.

Supervision and contact
This project is a cooperation of the Theory of Hybrid Systems research group led by Prof. Dr. Erika Ábrahám, and the Computational Nuclear Engineering (MathCCES) research group led by Prof. Dr. Martin Frank. The project will be co-supervised by Torsten Trimborn, M.Sc.

Contact
Torsten Trimborn, M.Sc.
Lehrstuhl für Mathematik (CCES)
Schinkelstr. 2, 52062 Aachen, 219 (Rogowski building, 2nd floor)
Tel.: +49-241-80-98671
Email: trimborn@mathcces.rwth-aachen.de