Computational Finance Numerical analysis for Stochastic PDEs in finance. Randomized Quasi-Monte Carlo method in pricing exotic options and mortgage backed security. Monte Carlo simulation of Asian option derivatives. Partial hedging in financial markets with a large agent using Bellman type PDE. Parameter estimation of a financial model using historical market data from CBOE (Chicago Board Options Exchange). Pricing of an American option and determination of optimal stopping time using Monte Carlo method. Fair pricing of an Asian option on weather derivatives. Interdisciplinary project ‘Antilium’, optimal design decisions on product portfolio valuation.
Finite Element Method Least squares method for stochastic PDEs. Numerical solutions and error analysis of SUPG method for a hyperbolic stochastic PDE. Numerical experiments of adaptive control least-squares method. Development of fixed grid adaptive least-squares method based upon least-squares principles in degenerate L2-norms. Improvement of L2-norm error estimates for the least-squares method. Comparison of Galerkin, SUPG and standard least-squares methods for a model convection problem. Development and analysis of finite element methods of least-squares type for hyperbolic partial differential equations.