Abstract: Stochastic compound risk has been applied widely in insurance claim theory,finance,economics and management. Mathematically,a stochastic compound risk can be expressed by a random sum. Risk premium is a very important concept in insurance economics and finance economics. It depends on the severity of risk and on the agency's risk attitude defined by utility function. In this paper,the premium of introducing stochastic compound risk has been studied on the expectation utility theory. The premium induced by compound numbers randomicity is measured. Moreover,introduing stochastic Poisson compound and stochastic Poisson-Geometric compound under some special utility functions,the premium has been analyzed and calculated.

Key words: stochastic compound risk, expectation utility theory, risk premium, stochastic Poisson compound, stochastic Poisson-Geometric compound