The Illustration for the Application of Asset Share in Premium

Abstract

With a case of whole life insurance, on the base of the actuarial theory of life insurance, this paper accounts for the theoretical foundation of the pricing method of asset share, establishes an intact theoretical framework, and simulates the process that the insurance company ascertains gross premium. In addition, for a real policy, the intact cash flow table is made out. This paper has valuable reference for further systematic study.

Key words: Premium; Asset share; Surplus; Profit; Cash flow

JI Zhirong, HE Dongjin (2013). The Illustration for the Application of Asset Share in Premium. Canadian Social Science, 9(2), -0. Available from: /index.php/css/article/view/j.css.1923669720130902.Z10210

DOI: /10.3968/ j.css. 1923669720130902.Z10210

INTRODUCTION

The calculation of premium is the kernel of actuarial theory of life insurance, and more crucial to product development. But now insurance market is filled with various insurances, and the additive method of net premium can’t meets requirements of the insurance company. So the insurance industry increasingly advocates the pricing method of asset share which is to be the mainstream. In this context, this paper applies asset share to test premium, makes an exploratory study on its theoretical foundations, and simulates the process that the insurance company ascertains gross premium with the pricing method of asset share.

With a case of whole life insurance, the paper firstly demonstrates the calculation of predetermined asset share and empirical asset share, whose difference implies potential profit; then analyzes the surplus; finally makes a case study on a practical whole life insurance policy particularly in terms of one marginal equilibrium year index in profit targets, evaluates the reasonability of the premium, works out relevant adjustment of premium, makes out the intact cash flow table and simulates the process that the insurance company ascertains gross premium.

Remark: In this paper the notations in the formulas are consistent with literature .

1. THE THEORY OF ASSET SHARE

Definition 1 Predetermined asset share is defined as asset on per valid policy reappraised by insurer, on the base of predetermined mortality, interest rate, surrender rate and expenses rate.

To the x-year-old man applying one unit whole life insurance policy, assuming death compensation, surrender value are given at the end of the year, according to the expenses and receipts equilibrium principle, we have

Definition 2 Because life insurance is usually a long contract, the change during the contract is difficultly predicted, the insurer takes conservative value to predetermined levels. Empirical asset share is defined as the asset due to practical empirical cost factor, also called empirical adjusted asset share.

Letbe the asset share of the yearby empirical cost factors on the base of . ,,,

,denote separately the corresponding effective value.

From the above, the difference between predetermined asset share and empirical asset share is made up of four parts: ①the difference of interest; ② the difference of expenses; ③the difference of mortality; ④the difference of surrender. Obviously we can see the potential profit of the insurer.

2. THE ANALYSIS OF SURPLUS

Comparing the calculation of empirical asset share and predetermined asset share, we can find the insurance premium is very conservative .As time goes on, operating profit can be predicted, which leads to the surplus, i.e. balance amount between asset and liability.

Let ,,be respectively the asset, the amount of liability and the amount of surplus at the end of the year . According to the asset balance principle, we have

(3)

For the sake of analysis, the definitions and computing formulas of net revenue and profit are given as follows:

Definition 3 Net revenue is defined as the benefit derived at the insurance year t for each unit valid policy at the end of each insurance year t , also called current profit and loss, generally denoted by S(t).

Then

Definition 4 Profit is defined as the profit of the year , which is equal to the value deducting the interest income of surplus from net revenue, and can be considered as the loss and profit which current business bring, generally denoted by.

Then

Net revenue containing more interest income is susceptible to the past operation, so profit can better account for the current operating.

When reserve is the only liability of the insurance company, surplus is the balance between asset share and reserve at the end of the year, then

3. The test of asset share in gross premium

For insurance companies, there are a number of factors to take into account when designing gross premium. Once the insurer sets the gross premium, he has to continuously monitor the influence of this particular deal on the company’s cash flow. By doing this, the insurer can determine whether or not the premium meets its target profit. The asset share provides the analytical basis for the insurance company. If the asset share generated by the experimental gross premium can’t meet the company’s goal, the gross premium will be raised, or particular policy interest (e.g. the death payment or cash value) will have to be reduced. On the contrary, if the asset share exceeds the expected, the insurer can cut down on the premium to attract more customers. For dividend-paying insurance and non-dividend paying insurance, the asset share can be adjusted by revising the experimental dividend and other non-contractual factors. Usually, the test of asset share in gross premium costs at best 20 or 30 years.

In short, to the test, we should first choose an experimental premium according to the fundamental factors comprising gross premium, and then evaluate whether it meets the targets of the insurance company. If not, we will adjust the factors and eventually reach the gross premium.

3.1 The Test of Target Profit

For the insurer, the major business objective is to make profits. Therefore, we will have to consider the reasonableness of gross premium in realization of target profit margin, if not, work out its adjusted formula by the calculation of asset share.

Several profit margin indexes are used in the test of asset share. Here we take one of them: marginal equilibrium year, i.e. the first year that surplus and accumulated profit is greater than 0, which is generally limited within 5 to 10 year, denoted by .

For the sake of analysis, we will provide the theoretical hypothesis: the reserve is the only liability item for the insurance company. Then the target profit is that the asset share of the nth year exceeds the reserve.

The following is the process of asset share testing gross premium on the marginal equilibrium year.

① Set the marginal equilibrium year and adjust the premium.

Choose the target of asset share to be K>nVx. Under certain insurance loading and cash value, we can calculate the gross premium G, and reach the asset share nAS at the end of the nth year according to the previously designed experimental gross premium H. The calculations are as follows:

The second item of Equation (10) can be considered as the adjusted value based on experimental gross premium.

② Analytical process

If the designed gross premium is reasonable, the initial asset shares will be less than the insurance reserve. This is because the actual expenses in the first few years tend to be relatively higher, and the number will decrease after several years. In this case, we can adjust the gross premium according to the target asset share value by adding insurance loading or deducting cash value from the gross premium.

If the initial asset shares greatly exceed the insurance reserve, the most possibility is that the actual expenditure is far less than the expected. In this circumstance, we will have to adjust the gross premium by adding cash value or deducting insurance loading from the gross premium.

③ Approximate the real value through repeated iteration.

Repeat step one and two, calculate the adjusted gross premium based on the target asset share, then adjust the insurance loading and cash value using computer software, in this way until ascertain the gross premium.

The above discussion can be considered as the epitome of the insurer using the asset share to test gross premium. Of course, in the real world, the insurance company will take into account other comprehensive factors when setting final gross premium.

3.2 Example Analysis

The following section will illustrate the process of asset share testing gross premium by a real example of whole-life insurance policy. We calculate the actual asset share, monitor the influence of experimental gross premium on the company’s cash inflows and outflows, analyze whether or not it meets the company’s target, and eventually explain validly the result.

Suppose company ABC is working on developing a kind of whole life insurance: the target customer is 35-year old man; the insurance amount will be 10,000 RMB; the premium will be paid out at the beginning of each insurance year.

Expected interest rate: i=0.06;

Insurance loading:

The first year is c1 equal to 30% of gross premium, and the succeeding year is c2 equal to 8% of gross premium;

The fixed-fee is e1 equal to 10 RMB for the first year, and e2 equal to 4 RMB for the succeeding years.

Cash value: according to the company’s empirical data is ;

The number of deaths is provided by the experimental life-span table;

The number of policy-holders canceling the contract is provided by the Linton A failure rate.

Suppose the surrendering action happens at the end of the insurance year, we can therefore have the effective insurance statistics.

To simulate the process of the asset share testing gross premium, Suppose:

The insurance amount is paid out at the end of year that the policy-holder died, and the surrender value is paid out at the end of year of cancellation.

The nation’s minimum legal standard of insurance reserve and cash value is considered when calculating insurance reserve and cash value.

1) Actuarial process

a). Deduce the experimental gross premium according to the company’s hypothesis:

3) Result analysis

a) Item N demonstrates gross premium is sufficient for the death payment, surrender value and all other expenses.

b) Item G is the actual cash value set by the insurance company, which is higher than the minimum legal cash value from the table 2. These demonstrate the actual cash value is quiet reasonable, which is consistent with the company's own operating requirements and is also not against minimum government requirement.

c) Item P is not an actual insurance reserve but the legal insurance reserve, refer to Table 1, the legal reserve is higher than the theoretical reserve. In the initial design of the gross premium, the insurance company should reach the standards of the supervision organization, and then take further amendment to insurance reserve, finally makes out actual reserve. Therefore, it is reasonable and desirable to illustrate the process of asset share testing gross premium by adopting legal insurance reserve.

d) Item Q shows that surplus of each valid insurance policy after one year of operation, and reflects the changes of assets. If the items of asset changing can’t meet the target of the insurance company or the standard of supervision organizations, the insurance company can alter the expected ratio in order to reach the target. However, high surplus for the policy appears at the first year, which means gross premiums may be high and the insurance loading is excessive.

e) Item U is the capital possessed by the valid policy when surrender occurred. At that time, the insured can only receive cash value not whole capital amount. The amount deducting cash value from asset share still belong to the valid insurance policy, which is a source of cash to insurance companies. Smaller U means less dependence on the surrender, so changes of surrender rate will not cause serious negative effects to the insurance company. Vice versa, larger U shows that the heavier dependence on the surrender, changes of surrender rate might adversely affect insurers. U for this policy has become increasingly dependent on surrender rate, which has to be modified.

4) Conclusion

The asset share analysis illustrates the influence of gross premium on cash flow. According to this, we determine that the gross premium is too high and requires adjustment.

The following adjusts the premium according to the marginal profit index: Let

The target asset share ;

Now we have the asset share based on the experimental gross premium:

According to formula (10), the adjusted premium:

The change of premium turns out to be 17.14 RMB. The gross premium after adjustment amounts to 80.04 RMB. From the perspective of marginal equilibrium year, the premium meets the requirement. Later, we have to modify the corresponding additional premium based on the adjusted gross premium. We repeat step one and continue to make the cash flow table and then compare the relationship between asset share and insurance reserve. Then we make adjustments with regard to the marginal equilibrium year and repeat the process, until finally reach the reasonable gross premium.

In the real world, the insurance companies have to take into account other profit targets when designing gross premium. And they would need to rely on computer software to perform substantial amount of tests before they come up with the appropriate gross premium.

CONCLUSION

On the base of primary actuarial theory, the paper makes an intact framework that asset share tests gross premium, simulates the pricing process of effective life insurance product (the pricing method of asset share). The method is quite complex and highly flexibility, which requires the professional skills of the insurer and computer proficiency. And the theoretical knowledge concerning insurance actuarial practice will be necessary. In the real world settings, this is traditionally accomplished by actuaries and other professional people.

To practical life insurance policy, this paper can help make a decision on the primary reasonability of premium, which is valuable reference for further systematic study.

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