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Study On Actuarial Theory And Method Of Life Insurance Under Random Rates Of Interest

Posted on:2005-11-15Degree:DoctorType:Dissertation
Country:ChinaCandidate:L Y WangFull Text:PDF
GTID:1116360122496890Subject:Operational Research and Cybernetics
Abstract/Summary:PDF Full Text Request
Usually the traditional actuarial theory is based on a fix interest rate with a purpose to simplify calculations. However, since the life insurance is a long-term economic action, the factors of government policy and economic cycles may cause the interest rate to be uncertain during the time of insurance, the study on actuarial theory and method under random rates of interest has become an important and popular topic. This thesis focuses on actuarial calculations of life insurance under random rates of interest, with emphasis on the most important problems such as calculation of insurance premium and reserving premium pick-up. It is divided into seven chapters.The first two chapters give introductions to the history of insurance, mathematical principle and research object are introduced briefly, The basic theory on rate of interest, survival function and life table, the methods for caculating insurance premium, the development and research of life insurance actuarial theory under random interest rate are also presented.In chapter 3, based on the characteristics of annuity, two methods are derived for calculating the expected value and variance of present values and the accumulation value of a class of annuity under random rates of interest of discrete type. Recurrence relations on the expected value and variance, and a simplified calculation formulas are obtained, than which is simple in structure and may be easily used for practical calculations.In chapter 4, considering that the influence of insurance premium of practical investment and unexpected accidents may effect the interest, the two models are established according to reflected Brownian motion model and the model combined with reflected Brownian motion and Poisson process, respectively. Various moments for present value of increasing life insurance are obtained, and the simplified formulas on calculating pure premium actuarial present value on the assumption of the uniform distribution of deaths are derived moreover. Numerical examples are given to demonstrate that the methods for constructing models are both rational and effective.In chapter 5, a new insurance program called family untied insurance is proposed. The model includes a couple's whole-life insurance, the compensation insurance of an early-death child, the pension of an old couple and the alimony for a child whose parents had died before he or she was 18 years old. The simplified formulas of balanced annual premium is obtained according to the following models: fixed interest rate, Wiener process model, reflected Brownian motion model and combined model of reflected Brownian motion and Poisson process with random interest rate, respectively. The simple formulas for actuarial present value of balanced annual premium are obtained under the condition of uniform distribution of deaths.In chapter 6, considering the pure insurance premium and the calculation of net premium reserves death rate is due to life table, rate of interest is taken by fixed rate of interest. In fact, there are some differences between life insurance death rate and death rate in mortality table, and rate of interest taken on randomness. The above differences and randomness can form profit and loss in insurance. MDIP method and generalized maximum entropy principle are used to decide the transcentdental distribution of life insurance rate of interest, and the Bayesian theorem is utilized to give the estimate of life insurance. Reflected Brownian motion is used to construct the model of random interest rate. We define the critical death rate of risk function and analyze the adventure of life insurance, hence provide the insurance company with method.In chapter 7, discusses the problem of dealing with insurance data, we consider the contamination distribution by the density function asf(x) = (1-a)fl(x) + qf2(x), when a and /, (x) is unknown. Adopt the way of non- parametric kernel density estimation to give en estimation of contamination coefficient a and /1 (x). And prove the estimation congruence. Finally a stochastic...
Keywords/Search Tags:random rates of interest, life insurance, annuity, actuarial present value, insurance, life function, reserve, risk function.
PDF Full Text Request
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