Duality-based a posteriori error estimates for some approximation schemes for optimal investment problems

Abstract

We consider a Markov chain approximation scheme for utility maximization problems in continuous time, which uses, in turn, a piecewise constant policy approximation, Euler–Maruyama time stepping, and a Gauß-Hermite approximation of the Gaußian increments. The error estimates previously derived in Picarelli and Reisinger (2018) are asymmetric between lower and upper bounds due to the control approximation and improve on known results in the literature in the lower case only. In the present paper, we use duality results to obtain a posteriori upper error bounds which are empirically of the same order as the lower bounds. The theoretical results are confirmed by our numerical tests.