Perturbed Linear-Quadratic Control Problems and Their Probabilistic Representations

TL;DR

This paper investigates nonlinear perturbations of stochastic linear-quadratic control problems, establishing links with backward stochastic differential equations and analyzing solution properties using stochastic control, PDEs, and BSDEs.

Contribution

It introduces new conditions for solvability and regularity of perturbed stochastic control problems through probabilistic representations.

Findings

Established conditions for problem solvability

Derived regularity properties of solutions

Linked control problems with BSDEs and PDEs

Abstract

We consider some certain nonlinear perturbations of the stochastic linear-quadratic optimization problems and study the connections between their solutions and the corresponding Markovian backward stochastic diferential equations (BSDEs). Using the methods of stochastic control, nonlinear partial differential equations (PDEs) and BSDEs, we identify conditions for the solvability of the problem and obtain some regularity properties of the solutions.