Realistic Modelling and Simulation of Financial Processes

Mathematical models of financial occurences like the famous and most widely used Black-Scholes model often make quite unrealistic assumptions on the market, such as lognormal returns, absence of transaction costs, unlimited liquidity, constant interest rates and volatilities as well as symmetric information. We aim to weaken some of these assumptions and try to get basic theoretical results as well as practical algorithms for the treatment of problems such as the valuation of classical and exotic derivative instruments. Quite often problems in finance can be reduced to the calculation of (sometimes very high-dimensional) integrals. For the practical algorithms we will therefor in most cases use Monte Carlo or quasi-Monte Carlo Methods.