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Demande de portefeuille et politique de couverture de risque sous information incomplète

  • Detemple, Jérôme

    (Faculty of management, McGill University)

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    In this paper, we consider two portfolio problems when information is incomplete and the investor wishes to maximize his utility of terminal wealth. Optimal portfolios are obtained in explicit form by using the Ocone and Karatzas (1991) representation formula for Wiener functionals under equivalent changes of measure. When terminal wealth results only from asset trading policies, the optimal portfolio has two components: one is a pure mean-variance term relative to the information of the investor, the other is a hedging component against revisions in the estimate of the drift of asset prices. For the Gaussian model, the hedging demand is related to the estimation error. When terminal wealth includes a random terminal cash-flow in addition to the cash generated by asset trading, we show that the optimal portfolio also includes hedging components against (i) stochastic fluctuations in the rate of growth of the terminal cash-flow and against (ii) revisions in the estimated drift of the rate of growth in the terminal cash-flow. Our formulas generalize diverse applications that have been considered in the literature. We conclude with a discussion of difficulties arising in models with asymmetric information. Dans cet article, nous considérons le problème de choix de portefeuille sous information incomplète lorsque l’investisseur maximise l’utilité de sa richesse terminale. Le portefeuille optimal est obtenu de manière explicite en utilisant la formule de représentation d’Ocone et Karatzas (1991) sous changement équivalent de mesure. Lorsque la richesse terminale découle uniquement de la politique d’investissement dans les actifs financiers, le portefeuille optimal a deux composantes : la première est un terme d’espérance-variance pur relatif à l’information de l’investisseur, la seconde un terme de couverture contre les fluctuations de l’estimateur de l’espérance de rendement des actifs financiers. Dans le cas du modèle gaussien, la demande de couverture est reliée à l’erreur d’estimation. Lorsque la richesse terminale provient également d’un cash-flow aléatoire en supplément des fonds générés par la politique d’investissement, nous démontrons que le portefeuille optimal contient aussi des termes de couverture contre (i) les fluctuations stochastiques dans le taux de croissance du cash-flow terminal et contre (ii) les révisions dans l’estimateur du taux d’appréciation du cash-flow terminal. Ces formules généralisent diverses applications considérées dans la littérature. En conclusion, nous abordons le problème d’information asymétrique.

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    Article provided by Société Canadienne de Science Economique in its journal L'Actualité économique.

    Volume (Year): 69 (1993)
    Issue (Month): 1 (mars)
    Pages: 45-70

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    Handle: RePEc:ris:actuec:v:69:y:1993:i:1:p:45-70
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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.
    2. Huang, Chi-Fu, 1985. "Information structure and equilibrium asset prices," Journal of Economic Theory, Elsevier, vol. 35(1), pages 33-71, February.
    3. Ioannis Karatzas & Xlng-Xlong Xue, 1991. "A Note On Utility Maximization Under Partial Observations," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 57-70.
    4. Detemple, Jerome B, 1986. " Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, American Finance Association, vol. 41(2), pages 383-91, June.
    5. Adler, Michael & Detemple, Jerome B, 1988. " On the Optimal Hedge of a Nontraded Cash Position," Journal of Finance, American Finance Association, vol. 43(1), pages 143-53, March.
    6. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    7. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
    8. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    9. Gennotte, Gerard, 1986. " Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-46, July.
    10. Stulz, René M., 1984. "Optimal Hedging Policies," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(02), pages 127-140, June.
    11. Detemple, Jerome B., 1991. "Further results on asset pricing with incomplete information," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 425-453, July.
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