Constrained stochastic MPC under multiplicative noise for financial applications

Motivated by financial engineering applications, we develop an interior point algorithm for a finite horizon probabilistically constrained stochastic linear-quadratic control problem under multiplicative noise. Under the assumption of affine state feedback, the stochastic problem is approximated by a nonlinear deterministic problem with the state being given by the mean vector and covariance matrix. Additionally, the probabilistic constraints are approximated using a log-normal distribution. The resulting nonlinear deterministic problem is tackled using an infeasible interior point method in which a Riccati difference equation can be utilized to significantly accelerate computations. A financial benchmark tracking problem is presented as a numerical example, and the fit of the log-normal approximation is assessed.