Abstract:
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 modeIled
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.
