2. Stochastic Models of Risk Management Concepts

The formulation and investigation of stochastic models for the fundamental quantitative concepts of risk management constitute the purpose of this chapter. The concepts of the main quantitative components of risk and the concepts of the main quantitative components of risk control and risk financing operations constitute the fundamental quantitative concepts of risk management. This chapter consists of two parts. The first part concentrates on the formulation and investigation of stochastic models for risk severity, risk duration, risk frequency, and total risk severity which are the main quantitative components of risk. The second part concentrates on the formulation and investigation of stochastic models for the time required for treating a risk occurrence, the time of the first occurrence of a major risk, the minimum time of a random number of risk occurrences, the number of ongoing risk occurrences, the multiplicative risk severity, and the riskiness which are the main quantitative components of risk control and risk financing operations.