A Dual Algorithm for Stochastic Control Problems: Applications to Uncertain Volatility Models and CVA

Abstract

We derive an algorithm in the spirit of Rogers [SIAM J. Control Optim., 46 (2007), pp. 1116--1132] and Davis and Burstein [Stochastics Stochastics Rep., 40 (1992), pp. 203--256] that leads to upper bounds for stochastic control problems. Our bounds complement lower biased estimates recently obtained in Guyon and Henry-Labordere [J. Comput. Finance, 14 (2011), pp. 37--71]. We evaluate our estimates in numerical examples motivated by mathematical finance.