Arbitrage and pricing functionals in financial market models

The objective of this research is to extend and investigate certain pricing methods for derivative products of the stock exchange. A basic result of mathematical finance states thatabsence of arbitrage opportunities implies the existence of so-called „risk-neutral” pricing rules. As in most cases there are several such pricing functionals it is important to find principles to choose one of them in the „right” way.

One such principle takes into account the subjective preferences of investors (described by the so-called utility functions) and determines the „right” price in accordance with these. Our aim is to extend these methods to a wider class of discrete-time market models and to investigate the continuity of these prices with respect to agents’ preferences.

Another field of research is the analysis of the so-called large financial markets: if there is no arbitrage in a market where agents dispose of a wide range of securities then certain relations between model parameters must hold. These relations can be subsequently used for pricing and arbitrage detection in e.g. bond markets.