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A note on log-optimal portfolios in exponential Lévy markets

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  • Hurd T. R.

Abstract

In this note we revisit Merton’s optimal portfolio selection problem in an exponential Lévy market, for an agent acting with a canonical utility function, the logarithm. As we show, the explicit optimal portfolios exhibit features similar to some of the pathological examples given by Kramkov and Schachermayer where certain discounted asset processes fail to be martingales. In our examples, these pathologies are seen to arise from natural shortselling and borrowing constraints imposed by the logarithmic utility.

Suggested Citation

  • Hurd T. R., 2004. "A note on log-optimal portfolios in exponential Lévy markets," Statistics & Risk Modeling, De Gruyter, vol. 22(3/2004), pages 225-233, March.
    • Handle: RePEc:bpj:strimo:v:22:y:2004:i:3/2004:p:225-233:n:4
    DOI: 10.1524/stnd.22.3.225.57066
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    References listed on IDEAS

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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
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    3. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 31-48, September.
    4. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    5. Fabio Bellini & Marco Frittelli, 2002. "On the Existence of Minimax Martingale Measures," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 1-21, January.
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