Classical Risk-Averse Control for a Finite-Horizon Borel Model

TL;DR

This paper establishes the existence of an optimal risk-averse controller for finite-horizon Borel models with non-linear dynamics and costs, using exponential utility, without state space augmentation, simplifying the solution approach.

Contribution

It proves the existence of an optimal controller in a complex setting without augmenting the state space, offering a more straightforward solution method.

Findings

Existence of an optimal risk-averse controller proven.

No need for state space augmentation in the solution.

Applicable to models with non-linear dynamics and non-quadratic costs.

Abstract

We study a risk-averse optimal control problem for a finite-horizon Borel model, where a cumulative cost is assessed via exponential utility. The setting permits non-linear dynamics, non-quadratic costs, and continuous state and control spaces but is less general than the problem of optimizing an expected utility. Our contribution is to show the existence of an optimal risk-averse controller without using state space augmentation and therefore offer a simpler solution method from first principles compared to what is currently available in the literature.