Distributionally robust Kalman filtering with volatility uncertainty

Understand

This work presents a distributionally robust Kalman filter to address uncertainties in noise covariance matrices and predicted covariance estimates.

• We adopt a distributionally robust formulation using bicausal optimal transport to characterize a set of plausible alternative models.
• The optimization problem is transformed into a convex nonlinear semi-definite programming problem and solved using the trust-region interior point method with the aid of $LDL^\top$ decomposition.
• The empirical outperformance is demonstrated through target tracking and pairs trading.