On the Role of the Growth Optimal Portfolio in Finance

Eckhard Platen ()

No 144, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: The paper discusses various roles that the growth optimal portfolio (GOP) plays in finance. For the case of a continuous market we showhow the GOP can be interpreted as a fundamental building block in financial market modeling, portfolio optimization, 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 coe±cient is introduced, controlling the amount invested in the savings account, which allows to characterize portfolio strategies that maximize expected utilities. Natural conditions are formulated under which the GOP appears as the market portfolio. A derivation of the intertemporal 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 generalize risk neutral and actuarial pricing. Finally, the GOP is described in various ways as the best performing portfolio.

Keywords: growth optimal portfolio; portfolio optimization; market portfolio; fair pricing; risk aversion coefficient (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cfn, nep-fin and nep-fmk
Date: 2005-01-01
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http://www.business.uts.edu.au/qfrc/research/research_papers/rp144.pdf (application/pdf)

Related works:
Journal Article: ON THE ROLE OF THE GROWTH OPTIMAL PORTFOLIO IN FINANCE (2005)
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Persistent link: http://EconPapers.repec.org/RePEc:uts:rpaper:144

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