Abstract:
The paper discusses various roles that the growth optimal portfolio (GOP) plays in finance. For the
case of a continuous market we show how the GOP can be interpreted as a fundamental building
block in financial market modeling, portfolio optimisation, contingent claim pricing and risk measurement.
On the basis of a portfolio selection theorem, optimal portfolios are derived. These allocate
funds into the GOP and the savings account. A risk aversion coefficient is introduced, controlling the
amount invested in the savings account, which allows to characterize portfolio strategies that maximise
expected utilities. Natural conditions are formulated under which the GOP appears as the market
portfolio. A derivation of the intcrtemporal capital asset pricing model is given without relying on
Markovianity, equilibrium arguments or utility functions. Fair contingent claim pricing, with the GOP
as numeraire portfolio, is shown to generalise risk neutral and actuarial pricing. Finally, the GOP is
described in various ways as the best performing portfolio.
