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.

中文翻译：

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置信集随时间变化的CRRA和CARA公用事业下的鲁棒的消费投资问题

在不变的相对风险规避和不变的绝对风险规避效用不变的情况下，我们考虑了一个健壮的消费投资问题。时变置信度集由Θ指定，即从[0，T ]到Lévy三胞胎的空间的对应关系，并描述先验漂移，波动率和跳跃信息。对于每种可能的度量，股票的对数价格过程都是半市场，它们的差分特征的三元组几乎可以肯定地是对应关系Θ中的一个可测量的选择器。通过提出和研究全局内核，从全局内核的鞍点生成了一个最优策略和一个最坏情况的度量，它们构成了目标函数的鞍点。