Abstract: The first part of the dissertation extends some important results in the classical theory of finite dimensional affine processes to infinite dimensional separable Hilbert spaces. In particular, a necessary and sufficient condition for a continuous Markov diffusion process to be affine...

In this note we present a simple method to include the no-arbitrage condition into the derivation of conditional densities using the principle of maximum entropy. For the case of identically and independently distributed returns, we easily derive that the whole process estimated that way is...

We use an information-theoretic approach to interpret Engle's (1982) and Bollerslev's (1986) GARCH model as a model for the motion in time of the expected conditional second power moment. This interpretation is used to show how these models may be generalized, if we use alternative measures of...

Information-theoretic approaches still play a minor role in financial market analysis. Nonetheless, there have been two very similar approaches evolving during the last years, one in so-called econophysics and the other in econometrics. Both generalize the notion of GARCH processes in an...

Generalized autoregressive conditional heteroskedasticity (GARCH) processes have become very popular as models for financial return data because they are able to capture volatility clustering as well as leptokurtic unconditional distributions which result from the assumption of conditionally...