DUALITY-BASED A POSTERIORI ERROR ESTIMATES FOR SOME APPROXIMATION SCHEMES FOR CONVEX OPTIMAL CONTROL PROBLEMS

Athena Picarelli (1) , Christoph Reisinger (1)

1 MI - Mathematical Institute [Oxford]

We consider a Markov chain approximation scheme for utility maximization in continuous time optimal investment problems, 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 A. Picarelli and C. Reisinger, Probabilistic error analysis for some approximation schemes to optimal control problems, arXiv:1810.04691, 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.

Domaines: Mathématiques [math]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Athena Picarelli, Christoph Reisinger. DUALITY-BASED A POSTERIORI ERROR ESTIMATES FOR SOME APPROXIMATION SCHEMES FOR CONVEX OPTIMAL CONTROL PROBLEMS. 2019. ⟨hal-01538617v2⟩