Conference abstracts

Session A7 - Stochastic Computation

July 10, 17:30 ~ 17:55

Approximation of BSDEs using random walk

Christel Geiss

University of Jyväskylä, Finland   -   christel.geiss@jyu.fi

For the FBSDE \[ X_t = x + \int_0^t b(r,X_r)dr + \int_0^t \sigma (r,X_r)dB_r \] \[ Y_t = g(X_T) + \int_t^T f(s, X_s,Y_s,Z_s)ds - \int_t^T Z_s dB_s, \,\,\,\, 0\le t \le T \]

Briand, Delyon and Memin have shown in [1] a Donsker-type theorem: If one approximates the Brownian motion $B$ by a random walk $B^n$, the according solutions $(X^n, Y^n,Z^n)$ converge weakly to $(X, Y, Z).$ \\ We investigate under which conditions $(Y^n_t,Z^n_t)$ converges to $(Y_t,Z_t)$ in $L_2$ and compute the rate of convergence in dependence of the H\"older continuity of the terminal condition function $g.$ \\

[1] P. Briand, B. Delyon, J. Memin, {\it Donsker-Type theorem for BSDEs.} Electron. Comm. Probab. 6, 1 -- 14 (2001).

Joint work with C\'eline Labart (Universit\'e de Savoie, France) and Antti Luoto (University of Jyv\"askyl\"a, Finland).

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