Research On Insurance Inestment And Contract Design

Uncertainty of insurance problems is shown mainly in highly risky and infor-mation asymmetry. Insurance problems under random environments have beenthoroughly studied and achieved great achievements. However, in real cases,uncertainties of insurance problems also includes fuzziness, randomness, fuzzyrandomness and so on, and the research of these aspects is still in its infancystage. Therefore, study of insurance problems under uncertain environmentswould be of great theoretic value and practical significance.This dissertation studies the problems of investment decision and contractdesign, and some models that more conforms to the practice are proposed. Spe-cific content as follows.Considering the characteristics of the insurance companies in the real worldthat the individual claim amount has not only randomness but also fuzziness,and that the investing activity and the claim activity are elegantly performedall at the same time, an investment model with an insurance and an investmentmodel with two insurances are built with the assumption that the individualclaim amount is a fuzzy random variable and the investment return rate is afuzzy variable. The optimal investment strategies are obtained by designing amonkey algorithm based on fuzzy simulation.For the problems of insurance contract design, where the insured (or patient)has some private information which is characterized as a fuzzy variable by theinsurance company (or public administration), a fuzzy deductible model, a fuzzycoinsurance model and a fuzzy waiting time model are built in this dissertation.In these models, the contract variables are devised with two dimensions. Thesethree models are converted to be control problems, and the necessary conditionsof the optimal solutions to the models are obtained by Pontryagin maximumprinciple.A fuzzy deductible contract model with an investment is built in a fuzzyenvironment, where the insurer can only give an assessment to the average loss of a special investment group, and the insured can merely give an assessmentto the investment loss, the investment return rate and the discount factor. Theoptimal investment strategies and the optimal deductible insurance are obtained.The problem of contract design with ex post asymmetric information of theinsurance companies is studied, an insurance employment contract model with aninsurer and an employed with property of overconfidence and underconfidence isconstructed within the framework of double moral hazard. The optimal contractsand the optimal e?orts are obtained, and the properties of the optimal contractand the optimal e?orts are analyzed by focusing on the confidence factors andthe relative importance factor.