Research On Several Problems About Insurance

The main problems which insurance reseach include premium pricing,insurance funds using,solvency regulation and the development of new products and so on.Much research about those problems has been done.The researchers establish some significant mathematical models and provide a lot of useful results.But in China,because insurance study just at begin,those models and results inevitablely have limitations.In this paper, in order to let those models become more realistic,we focus our work on improving those models and ginving further analysis.At last,some problems for future study are given which provide the direction of future research. This paper include six chapters.In order to achieve above goals,we study premium pricing problem based on investment theory,the optimal investment of insurance funds,ruin probability and a unit-linked life insurance model for embedding a surrender option under stochastic interest rate respectively.Firstly,we simply introduce the significance of insurance in national economy,the new age of insurance development and the research background, the main content and significance of this paper. The second chapter point out the backward stochastics differential equation accord with the thinking for mathematical finance research.BSED play an important part in the study in mathematical finance.Using the theory of BSED and its relative results,we establish premium pricing model based on investment theory and obtain the premium pricing formula. In the third chapter, using the time gaps between payment insurance and insurance indemnity,we study insurance funds investment,establish insurance investment model on continuous time in which reference of risk and management fee rate are considered. Moreover,the optimum investment propotion is obtained. The forth chapter research the solvency of insurance company on the basis of ruin theory.On the condition that police arrival and insurance indemnity follow Cox process,we establish a double Cox risk model with additional premium and obtain the upper bound of ruin probability.Furthermore,under the assumption that police arrival and insurance indemnity follow process with the same accumulate intension,we provide an explicit expression of the ruin probability formula. The fifth chapter establish a life insurance endowment police model.The model including a participation option and a surrender option under stochastic interest rate and the calculating formula of the value of each component is given.