Distributionally Robust Kalman Filtering Under Volatility Uncertainty

Summary

This work develops a Kalman filtering method for settings where noise covariance matrices and predicted covariance estimates are uncertain. It uses a distributionally robust formulation to account for plausible alternative models, with bicausal optimal transport defining the uncertainty set.

The resulting optimization is reformulated as a convex nonlinear semidefinite program and solved with a trust-region interior-point method using an LDL-transpose decomposition. The authors report empirical outperformance in target tracking and pairs trading. The excerpt does not specify the benchmarks, data, or evaluation measures, so it is not possible to assess how broad or statistically strong those gains are. The method’s practical value will depend on its assumptions about model uncertainty and the computational demands of its optimization.

Key ideas

• The filter addresses uncertainty in noise covariances and predicted covariance estimates.
• Bicausal optimal transport is used to define a set of plausible alternative models.
• The optimization is cast as a convex nonlinear semidefinite program.
• The method is evaluated in target tracking and pairs trading, though the excerpt gives no benchmark details.

Tags

# Distributionally robust Kalman filtering with volatility uncertainty


# Distributionally robust Kalman filtering with volatility uncertainty









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.