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-dY_{t}+H\\left(t,Y_{t}\\right) \\partial\\varphi\\left(Y_{t}\\right) \\left(dt\\right) \\ni F\\left(t,Y_{t},Z_{t}\\right) dt-Z_{t}dB_{t},\\quad t\\in\\left[ 0,T\\right] ,\\smallskip\\\\ Y_{T}=\\eta, \\end{array} \\right. \\] where $H$ is a bounded symmetric smooth matrix and $\\varphi$ is a proper convex lower semicontinuous function, with $\\partial\\varphi$ being 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