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Multi-Dimensional Backward Stochastic Ricatti Equations, and Applications

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  • Michael Kohlmann

    ()
    (Center of Finance and Econometrics)

  • Shanjian Tang

    ()
    (Center of Finance and Econometrics)

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    Abstract

    Multi-dimensional backward stochastic Riccati differential equations (BSRDEs in short) are studied. A closed property for solutions of BSRDEs with respect to their coefficients is stated and is proved for general BSRDEs, which is used to obtain the existence of a global adapted solution to some BSRDEs. The global existence and uniqueness results are obtained for two classes of BSRDEs, whose generators contain a quadratic term of L (the second unknown component). More specifically, the two classes of BSRDEs are (for the regular case N > 0)

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    Bibliographic Info

    Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 00-29.

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    Length: 27 Pages
    Date of creation: Sep 2000
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    Handle: RePEc:knz:cofedp:0029

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    1. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    2. Martin Schweizer & HuyËn Pham & (*), Thorsten RheinlÄnder, 1998. "Mean-variance hedging for continuous processes: New proofs and examples," Finance and Stochastics, Springer, vol. 2(2), pages 173-198.
    3. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
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