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arXiv · 0910.4213

Necessary and sufficient condition for the comparison theorem of multidimensional anticipated backward stochastic differential equations

Xiaoming Xu
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Abstract

Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type: {tabular}{rlll} $-dY_t$ &=& $f(t, Y_t, Z_t, Y_{t+\delta(t)}, Z_{t+\zeta(t)})dt-Z_tdB_t, $ & $ t\in[0, T];$ $Y_t$ &=& $\xi_t, $ & $t\in[T, T+K];$ $Z_t$ &=& $\eta_t, $ & $t\in[T, T+K].$ In this paper, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional anticipated backward stochastic differential equations with generators independent of the anticipated term of $Z$.

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Xiaoming Xu. 2009-10-22. Necessary and sufficient condition for the comparison theorem of multidimensional anticipated backward stochastic differential equations. https://doi.org/10.1007/s11425-010-4129-x

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