Optimal control of partially observable linear quadratic systems with asymmetric observation errors

This paper deals with the optimal quadratic control problem for non-Gaussian discrete-time stochastic systems. Our main result gives explicit solutions for the optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. For this purpose an asymmetric version of the Kalman filter based on asymmetric least squares estimation is used. We illustrate the applicability of our approach with numerical results

OPTIMAL CONTROL OF PARTIALLY OBSERVABLE LINEAR QUADRATIC SYSTEMS WITH ASYMMETRIC OBSERVATION ERRORS

This paper deals with the optimal quadratic control problem for non-Gaussian discrete-time stochastic systems. Our main result gives explicit solutions for the optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. For this purpose an asymmetric version of the Kalman filter based on asymmetric least squares estimation is used. We illustrate the applicability of our approach with numerical results.

On credibility and robustness with the Kalman filter

Bühlmann (1967) gave a formal Bayesian derivation of the credibility ratio estimators that actuaries had been using for many years. Since then various generalizations of Bühlmann's model have appeared in the literature, each relaxing the i.i.d. assumptions in its own way. The introduction of weights is due to Bülhmann & Straub (1970) and that the regressors to Hachemeister (1975), but the first comprehensive actuarial application of the Kalman filter is due to de Jong & Zehnwirth (1983). More recent efforts have concentrated on the robustification of these estimators, as they provedı to be extremely sensitive to large claims. Kremer (1991) studies a robust regression credibility model and Künsch (1992) tackles the weighted case. Following Kremer (1994) we propose here a robust Kalman filter credibility model

Inequalities for the ruin probability in a controlled discrete-time risk process

Ruin probabilities in a controlled discrete-time risk process with a Markov chain interest are studied. To reduce the risk there is a possibility to reinsure a part or the whole reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a constant stationary policy. The relationships between these inequalities are discussed. To illustrate these results some numerical examples are included

Identifying topological-band insulator transitions in silicene and other 2D gapped Dirac materials by means of R\'enyi-Wehrl entropy

We propose a new method to identify transitions from a topological insulator to a band insulator in silicene (the silicon equivalent of graphene) in the presence of perpendicular magnetic and electric fields, by using the R\'enyi-Wehrl entropy of the quantum state in phase space. Electron-hole entropies display an inversion/crossing behavior at the charge neutrality point for any Landau level, and the combined entropy of particles plus holes turns out to be maximum at this critical point. The result is interpreted in terms of delocalization of the quantum state in phase space. The entropic description presented in this work will be valid in general 2D gapped Dirac materials, with a strong intrinsic spin-orbit interaction, isoestructural with silicene.Comment: to appear in EP

Optimal policies for discrete time risk processes with a Markov chain investment model

We consider a discrete risk process modelled by a Markov Decision Process. The surplus could be invested in stock market assets. We adopt a realistic point of view and we let the investment return process to be statistically dependent over time. We assume that follows a Markov Chain model. To minimize the risk there is a possibility to reinsure a part or the whole reserve. We consider proportional reinsurance. Recursive and integral equations for the ruin probability are given. Generalized Lundberg inequalities for the ruin probabilities are derived. Stochastic optimal control theory is used to determine the optimal stationary policy which minimizes the ruin probability. To illustrate these results numerical examples are included

A parallel Kalman filter via the square root Kalman filtering

A parallel algorithm for Kalman filtering with contaminated observations is developed. Theı parallel implementation is based on the square root version of the Kalman filter (see [3]). Thisı represents a great improvement over serial implementations reducing drastically computationalı costs for each state update

Controlled diffusion processes with markovian switchings for modeling dynamical engineering systems

A modeling approach to treat noisy engineering systems is presented. We deal with controlled systems that evolve in a continuous-time over finite time intervals, but also in continuous interaction with environments of intrinsic variability. We face the complexity of these systems by introducing a methodology based on Stochastic Differential Equations (SDE) models. We focus on specific type of complexity derived from unpredictable abrupt and/or structural changes. In this paper an approach based on controlled Stochastic Differential Equations with Markovian Switchings (SDEMS) is proposed. Technical conditions for the existence and uniqueness of the solution of these models are provided. We treat with nonlinear SDEMS that does not have closed solutions. Then, a numerical approximation to the exact solution based on the Euler- Maruyama Method (EM) is proposed. Convergence in strong sense and stability are provided. Promising applications for selected industrial biochemical systems are showed