MITACS Math Finance Seminar 2007

  • Date: 10/11/2007
Lecturer(s):

Taflin Erik (University Paris—Dauphine, CEREMADE)

Location: 

University of British Columbia

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)

Other Information: 

MITACS Math Finance Seminar 2007

Sponsor: 

pimsmitacs