Global Adapted Solution of One-Dimensional Backward Stochastic Riccati Equations, with Application to the Mean-Variance Hedging
We obtain the global existence and uniqueness result for a one-dimensional back- ward stochastic Riccati equation, whose generator contains a quadratic term of L (the second unknown component). This solves the one-dimensional case of Bismut- Peng's problem which was initially proposed by Bismut (1978) in the Springer yellow book LNM 649. We use an approximation technique by constructing a sequence of monotone generators and then passing to the limit. We make full use of the special structure of the underlying Riccati equation. The singular case is also discussed. Finally, the above results are applied to solve the mean-variance hedging problem with stochastic market conditions.
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- 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.
- HuyËn Pham & Jean Paul Laurent, 1999. "Dynamic programming and mean-variance hedging," Finance and Stochastics, Springer, vol. 3(1), pages 83-110.
- 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.
- 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.
- Christian Gourieroux & Jean Paul Laurent & Huy�n Pham, 1998.
"Mean-Variance Hedging and Numéraire,"
Wiley Blackwell, vol. 8(3), pages 179-200.
- 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.
- Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
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