# Optimal Values for Calculation of Premium in Life Insurance

Cvetko Andreeski (Department of Tourism and Hospitality, University St. Kliment Ohridski – Bitola, Ohrid, Republic of Macedonia)
DOI: 10.4018/ijeoe.2013070105

## Abstract

Life insurance is very challenging sector in developing countries. Life insurance makes contribute at the investments in every country, so the more developed life insurance, more investments one should expect. One of the main aspects in calculation of risk in life insurance is using updated tables of mortality and forecast of the future values of mortality. There are many functions and models for mortality forecast calculation. Lee-Carter and Azbel Model for mortality trend calculation are used in this paper. In order to evaluate the results, data sets with the mortality in the Republic of Macedonia are used.
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## 2. Premium Calculation In Life Insurance

Calculation of life insurance takes in combination risk of mortality over the years and calculation of the interest because life insurance is long time insurance. From the literature we can see the model for calculating life insurance of insured sum for the risk of death over several years n. Model is given by (1)(Gerber 1997):

(1) Where is the probability of death during the age of x+j year and r=i+1, is the accumulation factor, and i is the interest rate calculated for the premium. If we calculate premium for the person old x=30 years in case of death in following n=10 years, we should use tables of mortality, or function of mortality. If we use table of mortality with its static values we should get higher risk of mortality than it is in real. The higher the calculated risk, the higher is the premium that insurance company calculated for that product of insurance. For example, if we take table of mortality of the Republic of Macedonia of 1994, and if we calculate interest value of 5%, we’ll get result of 0.022 units of premium to be paid per one unit of insured sum. If we make same calculation with the mortality tables of 2004, the result for the same type of insurance and all the same other parameters is 0.016. So, the calculated premium with the values of 1994 is 37.5% greater than the value calculated by the mortality tables of 2004. This is only one case of increased risk, but if in long terms, risk of mortality for the ages lower than 40 decreases during the years, and it increases the values as we analyze ages over 70. If we make further analysis, we’ll get the result that during the last 50 years, the life expectancy has increased for at least 10 years. So, it’s very important to have the proper prediction of the mortality for the next years. Because the life insurance is the long lasting, we should make predictions on large scale, and we should make adjustments on every 2-3 years.

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