## MITACS Math Finance Seminar 2007

- Date: 10/11/2007

Taflin Erik (University Parisâ€”Dauphine, CEREMADE)

University of British Columbia

The Mutual Fund Theorem (MFT) is considered in a general

semimartingale financial market $ with a finite time horizon T. It is established that:

1) If for given utility functions (i.e. investors) the MFT holds true

in all Brownian financial markets S then all investors uses the same

utility function U (modulo affine transformations), where U must be a

logarithmic or power utility function. This generalizes a result of Cas

and Stiglitz for discrete time markets.

2) Let N be the wealth process of the num'eraire portfolio (i.e. the

optimal portfolio for the log utility). If the market is such that all

path independent options on N with maturity T are replicable by trading

in N only, but using all information available in the market, then MFT

holds for 'all' utility functions. Moreover supposing

that all path independent options on N with maturity T are replicable

in the market S, also the converse of this statement is true. This

generalizes Mertons classical result on MFT in Black-Scholes markets.

(Joint work with M. Sirbu and W. Schachermayer)

**MITACS Math Finance Seminar 2007**