  In this paper, we study the existence of an optimal strategy for the
stochastic control of diffusion in general case and a saddle-point for zero-sum
stochastic differential games. The problem is formulated as an extended BSDE
with logarithmic growth in the $z$-variable and terminal value in some $L^p$
space. We also show the existence and uniqueness of solution of this BSDE.
