Moral Hazard,the Exponential-Zero Utility And The Generator Applied In Insurance

This paper studies the insurance contracts,the risk model of insurance and the premium strategy synthetically.We consider the function of inspire theory,stochastic analysis and functional analysis for those aspects of insurance forward.This paper mostly involves the Moral Hazard in inspire theory,Martingale theory in stochastic analysis and the semigroup theory in functional analysis.In the first chapter,we construct the contract model of complete competition market when the agent's utility is nonseparable in wealth and effort.We resolute the optimal insurance contracts by inducing the coefficient of absolute risk prudence.The model illustrates the conditions which involve the restrictions on distribution function ,the relation between absolute risk prudence and absolute risk averse .We also research the characters of the compensation and the insurance premium rate under the optimal insurance contracts.In the second chapter,we inducts the proportional reinsurance to risk model that is perturbed by diffusion,calculates the insurance premium of the reinsurance strategy by the exponential—zero utility principle. By the method of martingale, we prove the up-bound and formula on the ruin probability. We also analyze the fluctuant characters of insurance premium and the rationality of this principle under exponential distribution. Finally,we provide a numerical example.In the last section,we consider a kind of multiple line risk process driven by a stationary Markov process. Using the fruit owned by Zbigniew Palmowski[21],we find the appropriate martingale by the theories of infinite generator, By the method of martingale we prove the Cramer-Lundberg inequality on the ruin probability.