Stability of Some Applied Probability Models

In order to study a real process or system researcher has to choose an appropriate mathematical model. Usually one considers input-output models dealing with such probability theory applications as communication, reliability, queueing, inventory, finance, insurance and others. Modern period in actuarial sciences is characterized by consideration of complex systems, interplay of cost and reliability approaches and wide use of computers, therefore it is desirable to treat discrete-time models. They can give approximation to corresponding continuous-time ones. Moreover, in some cases they provide a better description of a real-life situation. So, we consider two discrete-time models and investigate their optimal performance and stability.