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We consider some certain nonlinear perturbations of the stochasticlinear-quadratic optimization problems and study the connections between theirsolutions and the corresponding Markovian backward stochastic diferentialequations (BSDEs). Using the methods of stochastic control, nonlinear partialdifferential equations (PDEs) and BSDEs, we identify conditions for thesolvability of the problem and obtain some regularity properties of thesolutions.

Perturbed Linear-Quadratic Control Problems and Their Probabilistic Representations