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On The Role Of The Growth Optimal Portfolio In Finance

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  • ECKHARD PLATEN

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 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 generalise risk neutral and actuarial pricing. Finally, the GOP is described in various ways as the best performing portfolio.

Suggested Citation

  • Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
  • Handle: RePEc:bla:ausecp:v:44:y:2005:i:4:p:365-388
    DOI: 10.1111/j.1467-8454.2005.00271.x
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    Citations

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    Cited by:

    1. Stein, Jerome L., 2007. "United States current account deficits: A stochastic optimal control analysis," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1321-1350, May.
    2. Michael J. Klass & Krzysztof Nowicki, 2010. "On The Consumption/Distribution Theorem Under The Long-Run Growth Criterion Subject To A Drawdown Constraint," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 931-957.
    3. David Heath & Eckhard Platen, 2005. "Currency Derivatives Under A Minimal Market Model With Random Scaling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1157-1177.
    4. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007.
    5. Christopoulos, Andreas D., 2017. "The composition of CMBS risk," Journal of Banking & Finance, Elsevier, vol. 76(C), pages 215-239.
    6. Liao Wang & Johannes Wissel, 2013. "Mean-variance hedging with oil futures," Finance and Stochastics, Springer, vol. 17(4), pages 641-683, October.
    7. Baldeaux Jan & Ignatieva Katja & Platen Eckhard, 2014. "A tractable model for indices approximating the growth optimal portfolio," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 1-21, February.
    8. Thomas Krabichler & Marcus Wunsch, 2021. "Hedging Goals," Papers 2105.07915, arXiv.org, revised Oct 2021.
    9. Pablo Castañeda & Heinz Rudolph, 2010. "Portfolio Choice, Minimum Return Guarantees, and Competition in DC Pension Systems," Working Papers 39, Superintendencia de Pensiones, revised Feb 2010.
    10. Rei[ss], Oliver & Schoenmakers, John & Schweizer, Martin, 2007. "From structural assumptions to a link between assets and interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 593-612, February.
    11. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 180, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. David R. Banos & Giulia Di Nunno & Frank Proske, 2013. "Sensitivity analysis in a market with memory," Papers 1312.5116, arXiv.org, revised Jan 2017.
    13. Eckhard Platen, 2005. "Investments for the Short and Long Run," Research Paper Series 163, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Muteba Mwamba, John & Suteni, Mwambi, 2010. "An alternative to portfolio selection problem beyond Markowitz’s: Log Optimal Growth Portfolio," MPRA Paper 50240, University Library of Munich, Germany.
    15. Lim, Andrew E.B. & Wong, Bernard, 2010. "A benchmarking approach to optimal asset allocation for insurers and pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 317-327, April.
    16. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 25, July-Dece.

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    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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