# Estimation of Generalized Linear Models Using Bayesian Approach in Actuarial Modeling

The article deals with Bayesian methodology for estimating unknown parameters of mathematical models and the method of analysis statistic data in insurance based on generalized linear models. These models are extension of linear regression when distribution of random variable can differ from normal. For estimating the parameters of proposed models classical and Bayesian approach were used. The main advantage of Bayesian approach is its ability to generate not only accurate estimates but probability distributions too.

# Optimization of Reinsurance Strategies Using DSS

The basic purpose of the work is a study of existing approaches to reinsurance directed towards modeling of distribution and minimization of risk for an insurance portfolio, and forming a strategy for its optimal reinsurance using developed decision support system. A method for a search of optimal reinsurance strategy is proposed. For this purpose statistical models were selected that correspond to the structure and volume of portfolio losses as well as the number of these losses. The simulation model for the total insurance losses is developed.

# Forecasting Actuarial Processes with Generalized Linear Models

The method for statistical data analysis in insurance based on application of generalized linear models is studied. These models are extension of linear regression when distribution of random variable can differ from normal however belongs to the class of elliptical distributions. The model constructed can be linear or non-linear (for example, logit or probit). For parameters estimation of the models proposed the generalized least squares (GLS) or the Markov chain Monte Carlo methods are used.

# Adaptive Short-Term Forecasting of Selected Financial Processes

A computer based system is proposed for adaptive modeling and forecasting of financial and economic processes, that is constructed with application of system analysis principles. A hierarchical structure of decision making process during forecasts estimation was taken into consideration and the methods were used for describing uncertainties of structural, parametric and statistical nature.

# Formalization of the Problem or Risk Management in Systems of Different Natures

The paper considers the problem of formal statement of the general problem of integrated risk management in complex systems as a whole of different nature. Relevance of such formulations caused with the fact that the existing approaches are directed to local non-systemic risk analysis that do not focus on different and often multidisciplinary nature of the risks, and are not able to overcome the problem of cascaded development of risks. The statement of the problem based on the Merton model is considered.

# Effective Implementation of the EM-algorithm using GPGPU

The problem of decreasing of running time for the data processing algorithms is very important especially when they are used in real time. For example, in real time image processing, process control systems, speech recognition, etc. The paper considers the possibility of decreasing running time of the expectation maximization (EM) algorithm using modern computing systems.

# Probabilistic Modeling of Operational Actuarial Risks

Insurance companies are functioning in conditions of uncertainties of various types and nature what results in respective financial risks. All these reasons lead to the problem of timely recognition and development of mechanisms for the risks management. To solve the problem appropriate mathematical models are developed to describe the risks, and methodologies proposed for their practical application. The sources of the insurance fraud are detected and respective risk classification is presented.

# A Scenario Approach to Modeling of the Pacific Trash Vortex

The study performed aimed at constructing and comparing scenarios of the solid waste treatment policy in different countries and their influence on variations of environmental dynamics changes in the area of ecological catastrophe – Pacific trash vortex. As input data for the scenario constructing and performing corresponding analysis the statistics for the solid waste processing in the USA, European Union and Singapore was used. The models were constructed for forecasting of the waste accumulated and the percentage of their processing.

# Forecasting Volatility of Financial Processes with Alternative Models

An analysis of modern approaches to modeling of conditional variance for nonstationary heteroscedastic processes is performed. A stochastic volatility model structure is proposed for multidimensional case and the methodology is considered for its parameter estimation with the use of Markov chain Monte Carlo technique. The use of this approach provides a possibility for parameter estimation of linear and nonlinear models in conditions of stochastic disturbance influence with various distributions of random variables.

# Modification and Application of Stochastic Volatility Model

A modified structure of autoregressive stochastic volatility model is proposed and empirically studied that includes delayed historical volatility values. The structure of the model developed is refined with the use of the partial autocorrelation function computed for sample values of the conditional variance process. The volatility logarithms correspond to the stationary autoregression process that provides a possibility for forecasting of the conditional variance dynamics with known model parameters.