Mathematisches Kolloquium

Zusammenfassung: We give a short review of the concepts and theory of Malliavin calculus for Levy processes and we show how it can be used to study various problems in a financial market driven by Levy processes. In particular, we give the following applications:

(i) When can a contigent claim in this market be hedged by a self-financing portfolio?

(ii) If a contigent claim cannot be hedged exactly, how do we find the portfolio which gives the closest hedge?

(iii) How does a trader find the portfolio which maximizes the expected utility of the terminal wealth when he has only PARTIAL information about the market?

(iv) Similarly, how does a trader find the utility maximizing portfolio if she has MORE information available than the information that can be obtained from the market? In other words, what is the optimal portfolio for an INSIDER in this market?

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