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Wittgenstein Award Laureate 1998 Univ. Prof. Dr. Walter Schachermayer

Stochastic processes in finance, Technical University of Vienna

Walter Schachermayer ext

Fakultät für Mathematik, Universität Wien
Department of Mathematics at the University of Vienna ext

mail walter.schachermayer@univie.ac.at

PURE MATHEMATICS AS A COMPETITIVE ADVANTAGE

Walter Schachermayer is applying the theory of random process to financial mathematics. This may sound rather abstract but it is in fact a useful tool, for example in the identification of arbitrage opportunities in the financial markets.

Schachermayer is modelling what actually happens in the stock exchange. ”There is a fundamental rule that says if it is not possible with absolute certainty to make a profit, i.e. if no – absolutely unfair – arbitrage is possible, you can describe stock trading or any similar game as a fair transaction.” In practice, chances can be distributed unevenly but it is possible to change the probabilities in the model ”in an equivalent way” so that it becomes a fair game. ”This is the technique behind the balancing regulations used in banks, that evaluate options or try to eliminate risks.”

This rule was postulated by economists at the end of the 70s. Schachermayer’s contribution was to develop a rigorous mathematical proof of it and this has been recognized as a crucial contribution to this field. The proof provides a framework within which the rules of the game are valid. It can thus be seen when they are not valid and – here comes the practical aspect – when someone might be able to identify arbitrage opportunities in the stock exchange. The governing principle is what Schachermayer and colleagues have described as, ”no free lunch with vanishing risk:” it should not be possible without capital input and without risk to make a profit in a risky environment. ”For dealers in options it is certainly a competitive advantage,” says Schachermayer, ”if they do not simply treat a model as a black box but instead understand the theory behind it. Such an understanding enables them to develop a feeling for when the underlying assumptions are violated.”

Schachermayer mentions the mathematics of insurance as a further focus of his research career. In this he has concentrated less on methodological originality than on practical relevance, ”on questions of balancing, so as to perform the various calculations for endowment or life insurance, where school mathematics alone is insufficient.”

The Wittgenstein Prize of 1998 enabled him to take ”quick and unbureaucratic decisions,” such as the hiring of pre- and post-docs from within Austria or abroad to carry out basic research relevant to ”concrete applications in the financial area.” It was also possible for him to bring Mark Davis, one of the most highly respected financial mathematicians, from England to Vienna for seven months before he took up his Chair at Imperial College. A profitable collaboration has developed with the dozen or so workers in Vienna, which has led to several joint publications.

Schachermayer is also planning a more intense and if possible institutionalized collaboration with his colleagues Peter Markowich (see page 66) and Georg Gottlob (page 36), both of whom are also the recipients of FWF support. It is planned jointly to found a ”Wolfgang Pauli Institute.”

Walter Schachermayer