The Dynamic Programming Equation for Second Order Stochastic Target Problems

Motivated by applications in mathematical finance [3] and stochastic analysis [16], we continue our study of second order backward stochastic equations (2BSDE). In this paper, we derive the dynamic programming equation for a certain class of problems which we call as the second order stochastic target problems. In contrast with previous formulations of similar problems, we restrict control processes to be continuous. This new framework enables us to apply our results to a larger class of models. Also the resulting derivation is more transparent. The chief technical tool is the geometric dynamic programming principle in this context and it is proved by using the framework developed in [18].