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University of Wuppertal
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University of Wuppertal
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Bilateral German-Slovakian Project
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The bilateral research project MACFIRE is a collaborative initiative between the University of Wuppertal in Germany and Comenius University in Bratislava, Slovakia. MACFIRE aims to address fundamental and applied challenges in computational finance by rigorously studying mathematical models and advanced numerical methods.
MACFIRE primarily focuses on analyzing and numerically approximating partial differential equations (PDEs) and forward-backward stochastic differential equations (FBSDEs). These equations arise in portfolio optimization, pricing complex financial derivatives, and financial risk management. Key topics include Hamilton-Jacobi-Bellman (HJB) equations, obstacle problems for American-style options, and pricing models under jump processes or Lévy dynamics. The project will develop efficient numerical schemes, such as semi-Lagrangian, Lagrange-Galerkin, and sparse grid methods, and study their convergence and stability properties.
MACFIRE leverages the complementary strengths of the German and Slovak teams in numerical analysis and stochastic modeling, respectively. There is a strong emphasis on involving young researchers through structured exchange visits, co-supervised theses, and joint seminars. MACFIRE will produce high-quality scientific publications, support the development of practical computational tools, and promote long-term academic cooperation and international research training in quantitative finance.
MACFIRE unites researchers whose expertise complements one another in the areas of mathematical modeling, partial differential equations (PDEs), stochastic analysis, and numerical methods. Together, they address pressing problems in computational finance. The project's primary objectives are to enhance theoretical knowledge and refine computational tools for intricate financial models. The focus is on analyzing and numerically treating differential equations that emerge in optimal control, option pricing, and stochastic processes in finance.
Computational finance is a rapidly evolving field that draws from a variety of disciplines, including probability theory, functional analysis, and numerical mathematics. Financial markets are influenced by various factors, including stochastic volatility, transaction costs, path dependence, and regulatory constraints. These factors challenge classical models and require more sophisticated mathematical approaches. MACFIRE addresses these challenges through the theoretical and computational study of PDEs, forward-backward stochastic differential equations (FBSDEs), and their applications to derivative pricing, optimal portfolio strategies, and financial risk management.
A central focus of MACFIRE is the rigorous analysis and numerical solution of nonlinear PDEs that arise in dynamic portfolio optimization and the valuation of path-dependent financial instruments. MACFIRE will study Hamilton-Jacobi-Bellman (HJB) equations resulting from stochastic control problems involving consumption, investment under constraints, or time-inconsistent preferences. These nonlinear PDEs often require careful treatment due to singularities, degeneracies, and free boundary conditions. Recent developments, such as Riccati-type transformations and viscosity solution frameworks, offer promising approaches for simplifying and analyzing their properties.
The project will examine the pricing of American-style and exotic options through the use of variational techniques and obstacle problems. The project will focus on shout options, swing options, and lookback derivatives because their nonlocal or memory-based features introduce significant computational complexity. These pricing problems usually result in variational inequalities that the teams will study using finite difference and finite element methods adapted to irregular domains. When incorporating jumps or Lévy processes into models, PDEs become partial integro-differential equations (PIDEs), adding another layer of complexity. The teams will develop and test numerical schemes that can handle such nonlocal terms efficiently and robustly.
German team:
Slovakian team: German institutions:
Slovakian institutions:
2026
2026
2026/2027
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