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

Zongxia Liang and Ming Ma

Mathematical Finance, 2020, vol. 30, issue 3, 1035-1072

Abstract: 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.

Date: 2020
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