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We consider a robust consumption-investment problem under CRRA and CARAutilities. The time-varying confidence sets are specified by $\Theta$, acorrespondence from $[0,T]$ to the space of L\'{e}vy triplets, and describepriori information about drift, volatility and jump. Under each possiblemeasure, the log-price processes of stocks are semimartingales and the tripletof their differential characteristics is a measurable selector from thecorrespondence $\Theta$ almost surely. By proposing and studying the globalkernel, an optimal policy and a worst-case measure are generated from a saddlepoint of the global kernel, and they also constitute a saddle point of theobjective function.

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