A Research On Life Insurance Model For Dependent Decrements

In the traditional model of life insurance, whether the insured lives is still insuredor not is uniquely determined by their remain lifetimes, that is, in the duration of theinsurance contract, the only causes for the insurer to violate the policy is the risk ofdeath, regardless of other causes of withdrawal. However, in practice, in addition tothe risk of death, the insurer is also affected by other risks. For example, disability,unemployment, disappearance，etc，which could cause the insured lives fail to pay intime, finally results in termination of the contacts，also the insurer may withdraw fromthe insurance because of other causes. Therefore, it is very significant to study themultiple decrement causes of life insurance model. However, in traditional lifeinsurance actuarial textbooks, for the multiple decrement causes model, it is assumedthat various decrement causes are independent, since it is convenient for the modeldeduction and the calculation of the decrement probabilities. In the reality, however,the decrement variables tend to be dependent. For instance, died one will no longer beconsidered in injure; or the injured one may accelerate his or her death. In this thesis,we study a life exposed to dependent causes of decrement, and also present someformula for computing the actuarial present values regarding this model. We furtherstudy two lives exposed to dependent causes of decrement, and also present someformula for computing the actuarial present values regarding this model. This thesis isorganized as follows:In Chapter One, we introduce the background and the significance of this projectas well as the development.In Chapter Two is the preliminary, which contains the definitions, properties andmeasure of the Copula function.In Chapter Three, based on the Copula function, we establish a decrement modelfor a life exposed to n dependent causes of decrement, and present the actuarialpresent values regarding this model.In Chapter Four, we mainly studies the survival probability for two lives exposed to n dependent causes of decrement, and also present some formula for computingthe actuarial present values regarding this model.In Chapter Five, we summarizes the research results and significance of thethesis, and points out the future research direction.