Duality and upper bounds in optimal stochastic control governed by partial differential equations

2017/04/30 by Shinji Tanimoto, Tanimoto, Shinji
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #math.OC

paper · pdf · doi:10.48550/arxiv.1705.00972

8 pages

arxiv created 2017/04/30 · arxiv updated 2017/05/03

Abstract

A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality theorems are proved. The dual problem serves to provide upper bounds for the optimal and maximum value of the original one or even to give the optimal value.

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