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|Abstract:||We study multidimensional BSDEs of the form Yt=ξ+∫Ttf(s,Ys,Zs)ds−∫TtZsdWs with bounded terminal conditions ξ and drivers f that grow at most quadratically in Zs. We consider three different cases. In the first case, the BSDE is Markovian, and a solution can be obtained from a solution to a related FBSDE. In the second case, the BSDE becomes a one-dimensional quadratic BSDE when projected to a one-dimensional subspace, and a solution can be derived from a solution of the one-dimensional equation. In the third case, the growth of the driver f in Zs is strictly subquadratic, and the existence and uniqueness of a solution can be shown by first solving the BSDE on a short time interval and then extending it recursively.|
|Citation:||Cheridito, Patrick, and Kihun Nam. "Multidimensional quadratic and subquadratic BSDEs with special structure." Stochastics: An International Journal of Probability and Stochastic Processes 87, no. 5 (2015): 871-884. doi:10.1080/17442508.2015.1013959|
|Pages:||871 - 884|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Stochastics: An International Journal of Probability and Stochastic Processes|
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