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Mean-Variance Efficiency and Intertemporal Price for Risk

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  • Leitner, Johannes

Abstract

In a continuous time, arbitrage free, non-complete market with a zero bond, we find the intertemporal price for risk to equal the standard deviation of the discounted variance opti- mal martingale measure divided by the zero bond price. We show the Hedging Numeraire to equal the Market Portfolio and find the mean-variance efficient portfolios.

Suggested Citation

  • Leitner, Johannes, 2000. "Mean-Variance Efficiency and Intertemporal Price for Risk," CoFE Discussion Papers 00/35, University of Konstanz, Center of Finance and Econometrics (CoFE).
    • Handle: RePEc:zbw:cofedp:0035
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    References listed on IDEAS

    as
    1. Leitner, Johannes, 2000. "Utility Maximization and Duality," CoFE Discussion Papers 00/34, University of Konstanz, Center of Finance and Econometrics (CoFE).
    2. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    3. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    4. Jean-Paul Laurent & Huyen Pham, 1999. "Dynamic programming and mean-variance hedging," Post-Print hal-03675953, HAL.
    5. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Martin Schweizer & Christophe Stricker & Freddy Delbaen & Pascale Monat & Walter Schachermayer, 1997. "Weighted norm inequalities and hedging in incomplete markets," Finance and Stochastics, Springer, vol. 1(3), pages 181-227.
    7. Christian Gourieroux & Jean Paul Laurent & Huyên Pham, 1998. "Mean‐Variance Hedging and Numéraire," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 179-200, July.
    8. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    9. Bismut, Jean-Michel, 1975. "Growth and optimal intertemporal allocation of risks," Journal of Economic Theory, Elsevier, vol. 10(2), pages 239-257, April.
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