German-Slovakian Project MATTHIAS on Hamilton-Jacobi-Bellman Equations in Finance
Bilateral German-Slovakian Project
MATTHIAS – Modelling and Approximation Tools and Techniques for Hamilton-Jacobi-Bellman equations in finance and Innovative Approach to their Solution
The project deals with qualitative and numerical analysis of nonlinear partial differential equations arising in mathematical finance. The main purpose is to develop new or to extend existing dynamic portfolio optimization models based on solving Hamilton-Jacobi-Bellman (HJB) equations, Black-Scholes equations for pricing financial instruments, as well as free boundary problems for advection-diffusion equations arising in financial mathematics. Specific research objectives include:
Analysis of qualitative and quantitative properties of solutions of nonlinear partial differential equation-based models arising in mathematical finance, proposing and analysing efficient numerical methods for their approximation and interpretation of the results in practice.
Specific research objectives
- Comparison of different numerical methods for solving Hamilton-Jacobi-Bellman equations. Qualitative and quantitative evaluation of various numerical methods.
- Investigating the viability of extending Hamilton-Jacobi-Bellman equation-based models from one-dimensional underlying process to a multi-dimensional one.
- Analysing nonlinear option pricing extensions based on Black-Scholes partial differential equation, Frey-Stremme partial integro-differential equations and free-boundary problems.
- Development and analysis of efficient numerical schemes for solving linear and nonlinear models with emphasis on models based on fully nonlinear parabolic PDEs including non-smooth diffusion terms.
These aims represent ongoing common research between the German team from Bergische Universität Wuppertal and the Slovak team from the Comenius University Bratislava entering this project proposal.
The industrial partner of this project, the GEFA bank, has the main office located in Wuppertal and a branch in Bratislava. This setting will offer the unique opportunity for mutual exchange between academia and industry, transfer of knowledge and also with the option for jointly supervised theses.
The webpage of this project can be found here.