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Recent Advances in Backward Stochastics Ricatti Equations and Their Applications

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  • Michael Kohlmann

    ()
    (Center of Finance and Econometrics)

  • Shanjian Tang

    ()
    (Center of Finance and Econometrics)

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    Abstract

    The following backward stochastic Riccati differential equation (BSRDE in short) is motivated, and is then studied. Some properties are presented. The existence and uniqueness of a global adapted solution to a BSRDE has been open for the case D i 6= 0 for more than two decades. Our recent results on this topic are summarized. Finally, applications are addressed, both in finance and control.

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    File URL: http://cofe.uni-konstanz.de/Papers/dp00_30.pdf
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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 00-30.

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    Length: 25 Pages
    Date of creation: Oct 2000
    Date of revision:
    Handle: RePEc:knz:cofedp:0030

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    1. 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.
    2. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    3. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    4. 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.
    5. 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.
    6. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
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