MITACS Math Finance Seminar 2007
Topic
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)
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)
Speakers
Additional Information
MITACS Math Finance Seminar 2007
Taflin Erik (University Paris—Dauphine, CEREMADE)
