Risk management decision making based on random sums incorporating thinned renewal processes in random times

The contribution of stochastic models to the development of risk management as a fundamental organizational discipline has been proved extremely important. It is now generally accepted that stochastic models are the most powerful analytical tools for evaluating the issues and alternatives and charting courses of action of an efficient risk management program. The main purpose of the present paper is to establish properties and applications in risk management decision making related to total risk severity measurement of a new stochastic model, which is based on a thinned stochastic renewal process and the product of two continuous, independent and nonnegative random variables.