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STOCHASTIC STABILITY AND OPTIMAL CONTROL OF SEMI-MARKOV RISK PROCESSES IN INSURANCE MATHEMATICS
                                                                             ANATOLY SWISHCHUK
                                                            Intern. Mathem. Center, Institute of Mathem.,
                                                            National Acad. of Scien. of Ukraine, Kiev, Ukraine
                 Abstract: We study semi-Markov risk processes which describe a dynamic of summary capital
                 of an insurance company. The theorems on stability, asymptotic and exponential stability of zero
                 state of the processes with probability 1 are proved. We also investigate the optimal stochastic
                  control of the controlled semi-Markov processes. The Bellman equation for semi-Markov risk
                 processes is derived. Analogue of Dynkin formulae and boundary value problem for semi-Markov
                random evolutions, and properties of the respected stochastic Liapunov functions are used.

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关键词：Exponential mathematics Probability Stochastic Controlled insurance describe dynamic capital company