Robust Bayes Premium Under Generalized Weighted Balanced-type Loss Function

The classical Bayes premium is built on the basis of quadratic loss function.However, in common insurance practice,we require that the principles of premium possess not only the property of fairness and rationality,but also the property of adequacy,flexibility and stability.In this dissertation,we discuss the principles of premium under generalized weighted balanced-type loss function.Individual premium,collective premium and Bayes premium researched by G(?)mez-Deniz(2007)don't meet the requirement of the common definition,so revisions are made in this dissertation.The revised Bayes premium has many good properties,such as non-negative safety additivity,constant additivity and consistence.Since Bayes premium is inestimable,further researches are based on the following special cases:(1).estimated premium with linear form of experience data(2).estimated premium with linear form of experience individual premium(3).estimated premium with regression form(the estimated parameter is a constant,with an easy and generalized form)(4).estimated premium with linear regression formFinally,by introducing two man-made variables we transform the expectation of generalized weighted balanced-type to the expectation of quadratic loss function.And simultaneously,in the use of posteriorΓ—minimax principle,we obtain robust Bayes premium under incomplete or inaccurate prior probability.