Bergische Universität Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Angewandte Mathematik - Numerische Analysis (AMNA)


Bilateral German-Slovakian Project

ENANEFA - Efficient Numerical Approximation of Nonlinear Equations in Financial Applications

financed by DAAD and the Slovakian Ministry of Education

(01/2018 - 12/2019)

Scientific goals

The project is focused on qualitative and numerical analyses of fully nonlinear partial differential equations (PDEs) of parabolic type arising in financial mathematics. The main purpose is to analyze non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, free boundary problems for advection-diffusion equations arising in financial mathematics as well as models of stochastic dynamic portfolio optimization based on the Hamilton-Jacobi-Bellman (HJB) equation.

Main objective:

Analysis of qualitative properties of solutions of nonlinear parabolic partial differential equations arising in financial mathematics, their efficient numerical approximations and interpretation of the results in practice.

Project tasks:

  1. Qualitative and numerical analysis of the HJB equation based on the direct approach and the Riccati transformation approach.
  2. Analysis of PDEs arising in interest rate models and their calibration. Development of new analytic approximations for solution to multi-factor and multi-dimensional models.
  3. Development and analysis of advanced stable numerical schemes for linear and nonlinear derivative pricing models.
  4. Free boundary problems in derivative pricing models and their efficient numerical tracking using the penalty method adjusted to the early exercise free boundary profile.

Specification of objectives and secondary objectives:

The secondary objective is to derive results on existence of solutions and their sensitivity on parameters. Analysis of the properties of the value function of a non-linear programming problem representing the nonlinear diffusion function of the parabolic PDE. Development of new stable numerical solution schemes for quasi-linear parabolic PDEs with non-smooth coefficients and backward diffusion equations as well as multidimensional advection tensor diffusion equations. Calibration of nonlinear models to real data and sensitivity analysis of solutions. Interpretation of the results obtained in practice.

Due to the multidisciplinary composition of the team members and their experience, international cooperation and involvement in international research projects we consider proposed goals as realistic as far as the scientific and time perspectives are concerned.

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.

German team:

Slovakian team:

German institutions:

Slovakian institutions:

Publications related to the Project



Talks related to the Project



Staff Exchange


Activities related to the Project

Former Projects

University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics
Applied Mathematics & Numerical Analysis Group

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