A dual algorithm for stochastic control problems: Applications to Uncertain Volatility Models and CVA

TL;DR

This paper introduces a dual algorithm to compute upper bounds for stochastic control problems, specifically applied to Uncertain Volatility Models and CVA, complementing existing lower estimates and validated through financial numerical examples.

Contribution

The paper presents a novel dual algorithm for stochastic control problems that provides upper bounds, enhancing the existing methods by complementing lower biased estimates.

Findings

Algorithm effectively computes upper bounds in financial models.

Numerical examples demonstrate practical applicability.

Complementary to existing lower estimates.

Abstract

We derive an algorithm in the spirit of Rogers and Davis & Burstein that leads to upper bounds for stochastic control problems. Our bounds complement lower biased estimates recently obtained in the work of Guyon & Henry-Labord\`ere. We evaluate our estimates in numerical examples motivated from mathematical finance.