Extreme Values of Gaussian Processes and A Heterogeneous Multi Agents Model

This PhD thesis consists of two parts that both can be put into a financial context. In the first part we consider the extreme behavior of a certain class of Gaussian processes. We are interested in the probability that a linear combination of Gaussian processes and adeterministic trend exceed a given high boundary. The result of this stochastic problem can be interpreted as the ruin probability of a portfolio of assets. In the second part we introduce the “Heterogeneous Multi Agents Model ” which describes the price process of avirtual foreign exchange market. The goals are to reproduce the statistical properties of price time series of real foreign exchange markets and to support the hypothesis of a heterogeneous market