Robust consumption-investment problem Under CRRA and CARA utilities with time-varying confidence sets

We consider a robust consumption-investment problem under CRRA and CARA utilities. The time-varying confidence sets are specified by Theta, a correspondence from [0,T] to the space of L'evy triplets, and describe priori information about drift, volatility and jump. Under each possible measure, the log-price processes of stocks are semimartingales and the triplet of their differential characteristics is a measurable selector from the correspondence Theta almost surely. By proposing and studying the global kernel, an optimal policy and a worst-case measure are generated from a saddle point of the global kernel, and they also constitute a saddle point of the objective function.