Discrete-Time Approximation of Risk-Averse Control Problems for Diffusion Processes

TL;DR

This paper develops a discrete-time approximation method for risk-averse control problems involving diffusion processes, using mollification and perturbation techniques to bound the difference in optimal values.

Contribution

It introduces a novel approximation framework for risk-averse control problems with diffusion processes, focusing on piecewise-constant controls and regularized value functions.

Findings

Bound on the difference between original and approximated optimal value functions

Construction of perturbed systems with piecewise-constant controls

Regularization technique for value function approximation

Abstract

We consider optimal control problems for diffusion processes, where the objective functional is defined by a time-consistent dynamic risk measure. We focus on coherent risk measures defined by $g$-evaluations. For such problems, we construct a family of time and space perturbed systems with piecewise-constant control functions. We obtain a regularized optimal value function by a special mollification procedure. This allows us to establish a bound on the difference between the optimal value functions of the original problem and of the problem with piecewise-constant controls.