# Feedback optimal controllers for the Heston model

## TL;DR

This paper establishes the existence of an optimal feedback controller for a modified Heston model with stochastic inputs, using advanced mathematical techniques to solve a nonlinear backward parabolic equation.

## Contribution

It introduces a novel stochastic control framework for the Heston model and proves the existence of solutions using martingale problem methods.

## Key findings

- Existence of an optimal feedback controller for the modified Heston model.
- Solution of a nonlinear backward parabolic equation with martingale solutions.
- Extension of stochastic control techniques to complex financial models.

## Abstract

We prove the existence of an optimal feedback controller for a stochastic optimization problem constituted by a variation of the Heston model, where a stochastic input process is added in order to minimize a given performance criterion. The stochastic feedback controller is searched by solving a nonlinear backward parabolic equation for which one proves the existence of a martingale solution.