Studies On Insurance Actuarial Theory And Applications

This dissertation is devoted to the study of insurance actuarial theory and its applications. The main works obtained in this dissertation are summarized as follows:1 Summarization of insurance actuarial theoriesReview the history of insurance actuarial science and its development and introduce its basic theories. Study the status and trend of international insurance market and that in our country.2 The aggregate model of life insuranceEstablish an aggregate model of life insurance by applying the alien modernly insurance actuarial theories and techniques, including deferred life annuities, whole life insurance and returnable premiums. The model has the following properties:(a) Through the regulation of various parameters in the model, various insurance products can be obtained;(b) The introduction of whole life annuities in the model eases economic predicament when the insured retire;(c) A returnable premium part in the model makes the insurance products have double functions of insurance and savings;(d) An endowment insurance actuarial model also can be gotten when annuity is continuous.And construct an optimization model based on aggregate model of life insurance.3 Aggregate model of life insurance with stochastic interestConstruct an aggregate model of life insurance with stochastic interest aiming at both the randomness of interest in practice and the importance of stochastic interest in life insurance. The introduction of stochastic interest in the model lessen risk of insurance company. The insurance company can also acquire various insurance products withstochastic interest by different combinations of parameters. Establish a stochastic optimization model based on aggregate model of life insurance with stochastic interest.4 The optimal insurance based on game theoryStudy the above aggregate model of life insurance by applying the game theories. The insurance process is characterized by the game of two-person zero-sum for the first time: The existence of the optimal value of premium in the model and how to obtain the optimal value are analyzed in detail based on the game theories. The game theory provides a new scientific method so as to determine an optimal premium between the insured and the insurance company. The insurance company can apply the model to dummy the premium, investigate market, obtain the optimal premium and determine the optimal insurance product accordingly.5 Utility and optimal game of insuranceApply the utility theory to insurance in order to confirm the optimal insurance premium for the insured.