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

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

Improving quality assessment of composite indicators in university rankings: a case study of French and German universities of excellence

Composite indicators play an essential role for benchmarking higher education institutions. One of the main sources of uncertainty building composite indicators and, undoubtedly, the most debated problem in building composite indicators is the weighting schemes (assigning weights to the simple indicators or subindicators) together with the aggregation schemes (final composite indicator formula). Except the ideal situation where weights are provided by the theory, there clearly is a need for improving quality assessment of the final rank linked with a fixed vector of weights. We propose to use simulation techniques to generate random perturbations around any initial vector of weights to obtain robust and reliable ranks allowing to rank universities in a range bracket. The proposed methodology is general enough to be applied no matter the weighting scheme used for the composite indicator. The immediate benefit achieved is a reduction of the uncertainty associated with the assessment of a specific rank which is not representative of the real performance of the university, and an improvement of the quality assessment of composite indicators used to rank. To illustrate the proposed methodology we rank the French and the German universities involved in their respective 2008 Excellence Initiatives.Composite indicators, Rankings, Benchmarking, Higher education institutions, Weighting schemes, Simulation techniques

Sensitivity and robustness in MDS configurations for mixed-type data: a study of the economic crisis impact on socially vulnerable Spanish people

Multidimensional scaling (MDS) techniques are initially proposed to produce pictorial representations of distance, dissimilarity or proximity data. Sensitivity and robustness assessment of multivariate methods is essential if inferences are to be drawn from the analysis. To our knowledge, the literature related to MDS for mixed-type data, including variables measured at continuous level besides categorical ones, is quite scarce. The main motivation of this work was to analyze the stability and robustness of MDS configurations as an extension of a previous study on a real data set, coming from a panel-type analysis designed to assess the economic crisis impact on Spanish people who were in situations of high risk of being socially excluded. The main contributions of the paper on the treatment of MDS configurations for mixed-type data are: (i) to propose a joint metric based on distance matrices computed for continuous, multi-scale categorical and/or binary variables, (ii) to introduce a systematic analysis on the sensitivity of MDS configurations and (iii) to present a systematic search for robustness and identification of outliers through a new procedure based on geometric variability notions.Gower distance, MDS configurations, Mixed-type data, Outliers identification, Related metric scaling, Survey data

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.Risk process, Ruin probability, Proportional reinsurance, Lundberg`s