Asymmetric Observation Errors in Optimal Control of Stochastic Quadratic Linear Systems and Application to Modelling Volatility

The case of partial observations with asymmetric errors (non-Gaussian) in dynamic systems is studied and an approximation for the solution is given. Controlled quadratic linear dynamic systems are considered. We also consider the situation with outliers, and a robust approximation for this case is proposed. This methodology could be used to represent the dynamic properties of financial time series when one wishes to estimate the unobserved volatility of the series.