Kalman Filter Learning Algorithms and State Space Representations for Stochastic Claims Reserving

Approximate Kalman Filter Q-Learning for Continuous State-Space MDPs

We seek to learn an effective policy for a Markov Decision Process (MDP) with continuous states via Q-Learning. Given a set of basis functions over state action pairs we search for a corresponding set of linear weights that minimizes the mean Bellman residual. Our algorithm uses a Kalman filter model to estimate those weights and we have developed a simpler approximate Kalman filter model that ...

Rotated Unscented Kalman Filter for Two State Nonlinear Systems

In the several past years, Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) havebecame basic algorithm for state-variables and parameters estimation of discrete nonlinear systems.The UKF has consistently outperformed for estimation. Sometimes least estimation error doesn't yieldwith UKF for the most nonlinear systems. In this paper, we use a new approach for a two variablestate no...

State Space Models and the Kalman Filter

Stochastic Claims Reserving in General Insurance

This paper considers a wide range of stochastic reserving models for use in general insurance, beginning with stochastic models which reproduce the traditional chain-ladder reserve estimates. The models are extended to consider parametric curves and smoothing models for the shape of the development run-off, which allow extrapolation for the estimation of tail factors. The Bornhuetter-Ferguson t...

Initializing the Kalman Filter for Nonstationary State Space Models

The Kalman filter cannot be used with nonstationary state space models. To circumvent this difficulty, a conditional state space model and a new algorithm, calIed the conditional Kalman filter, can be used. The conditional state space model is obtained by first selecting adequately that part oof the initial state vector which has an unspecified distribution and then conditioning on O. Using the...