Optimal investment and consumption problems under correlation ambiguity

Abstract

Abstract Consider an economy with $d$ stochastic factors that have an ambiguous variance–covariance matrix. An ambiguity- and risk-averse agent seeks to determine the optimal investment and consumption strategy that is robust to the uncertainty in the covariances. We formulate the robust decision rule as an expected utility maximization over the worst-case scenario with respect to all possible covariances. As this variance–covariance ambiguity leads to robust optimal decisions over a set of non-equivalent probability measures, the $G$-expectation framework is adopted to characterize the problem as a maximin optimization. Our problem formulation can be applied to finite and infinite horizon investment–consumption problems with or without a subsistence consumption constraint. We demonstrate our models using two examples including the defined contribution pension problem and lifetime optimal investment–consumption problems.