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

We consider a robust consumption-investment problem under constant relative risk aversion and constant absolute risk aversion utilities. The time-varying confidence sets are specified by Θ, a correspondence from [0, T] to the space of the Lévy triplets, and describe a priori drift, volatility, and jump information. For each possible measure, the log-price processes of stocks are semimartingales, and the triplet of their differential characteristics is almost surely a measurable selector from the correspondence Θ. By proposing and investigating the global kernel, an optimal policy and a worst-case measure are generated from a saddle point of the global kernel, and they constitute a saddle point of the objective function.