BFS 2002 |
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Contributed Talk |
Eckhard Platen
This paper introduces a benchmark approach for the
modelling of continuous, complete financial markets when an
equivalent risk neutral measure does not exist. This approach is
based on the unique characterization of a benchmark portfolio, the
growth optimal portfolio, which is obtained via a generalization
of the mutual fund theorem. The discounted growth optimal
portfolio with minimum variance drift is shown to follow a Bessel
process of dimension four. Some form of arbitrage can be
explicitly measured by arbitrage amounts. Fair contingent claim
prices are derived as conditional expectations under the real world
probability measure.
The Heath-Jarrow-Morton forward rate
equation remains valid despite the absence of an equivalent risk
neutral measure.