Considering The Interests Of The Insurance Company's Optimal Insurance Problems

With the rapid development of the insurances,the research of it become perfect.Now usually the optimal insurance is determined by the maximization of the insured' s expected utility or the minimization of his/her residual risk under different premiumprinciples.Little attention has been paid on the controlling of the insurer' s risk exposure.In the article, we make use of the article of Zhou (2007) Gajeek (2004) and Young (1999)to consider imposing the insurer' s risk constraint on the optimal insurance problem.This dissertation consists of four chapters.Chapter one is the preface,we introducethe models under discussion.The models are maximize the insured's expectedutility under the insurer's risk constraint.Chapter two,we when the premiumis mean-variance principles,the form of I^*(x).When I^*(x) is in different section,what condition x should satisfied. meanwhile, we give an example. When u(x) = -(x -W₁+ EX)²,we give the subsection of I^*(x).Chapter three we discuss the optimal insurance under Wang's premium principles.Chaper four we don't only focus on the expected utility of the insured,but also focus on the expected utility of the insurers.