Optimal regulator for a class of nonlinear stochastic systems with random coefficients

We consider an optimal regulator problem for a class of nonlinear stochastic systems with a square-root nonlinearity and random coefficients, and using the quadratic-linear criterion. This represents a certain nonlinear generalisation of the stochastic linear-quadratic control problem with random coefficients. The solution if found in an explicit closed-form as an affine state-feedback control in terms of a Riccati and linear backward stochastic differential equations. As an application, we give the solution to an optimal investment problem in a market with random coefficients.