New developments in stochastic maximum principle and related backward stochastic differential equations

The author presents some developments in the stochastic maximum principle of optimal control theory. Progress on backward stochastic differential equations that relates tightly to the stochastic maximum principle is discussed. It is shown that theory continues to keep a close relation to classical variational methods and Hamiltonian systems and its own special stochastic character. For this reason, the subject remains vigorous, not only by virtue of its important practical applications, but also because it motivates other applied mathematical and practical problems