The risks are measured or evaluated for fixation of premium be charged by the insurer. Let’s know detail about the measurement of risk and mortality table. And firstly we discuss the method of calculation of premium. There are two methods of calculation of premiums.

- The value of service,
- Cost of Service.

## Methods of calculation of premium

**1. The value of service**

The value of service determines the rate of the premium according to the utility of insurance to each proponent. Since the value or utility to each person differs; the premium rate will also vary.

The value of service principle cannot be used in insurance because its utility to each individual cannot be determined.

Moreover, the value is higher to the proper section of society and to the head of a large family; but they cannot be charged a higher premium than the premium charged by the richer class of the society.

Moreover, the higher premium will not attract business from them. The value of service cannot be used due to its impracticability.

**2. The cost of Service**

In fact, the premium should be charged according to cost to the insurer. In insurance, the demand side does not play an important role.

Therefore, it is called that the insurer is no bought, but it is sold. So, the insurer must fix the cost or premium to be charged for a particular risk or policy. Insurance businesses may carry on only when the cost of insurance is met.

The cost includes all expenses of the business plus a small profit margin. Above the profit margin, an insurer is not expected to gain.

This is the reason that the insurance business is expected to run on no loss, no gain, and a basis. The most important cost to an insurer is the cost of a claim.

Therefore, the insurer must charge at least so much of premium that can be used to pay the full amount of the claim.

Therefore, the insurer must charge at least so much of premium that can be used to pay the full amount of the claim.

Technically, the premium charged to meet the amount of claim, is called the net premium. Another cost to an insurer is the cost of administration.

It includes all expenses of management and another amount for provisions of contingency.

The cost of administration may be of two types,

- Fixed cost, and
- Recurring cost.

The Fixed cost is spread over the policy life but the recurring expenses do not involve many problems of allocation.

The method of the expenses is called loading which, is discussed in detail in a separate chapter.

With the help of loading, a net premium is enhanced to charge a fixed amount regularly from the policyholders, which is called gross premium is enhanced to charge a fixed amount regularly from the policy-holders, which is called gorses premium or office premium or office premium.

So, the first problem before the insurer is to calculate the cost of claims.

## Cost of Claims

The claims may arise at the death of the life assured or at the of the policy. In an annuity contract, the payment shall continue to death, therefore, the expectation of survival will be the basis of the cost.

In life insurance, in most cases, payment of claims depends upon death. death is certain but when it will take place is not certain.

Therefore, the main problem before the insurer is to decide when death will take place. The forecasting of death is a very important factor to decide the period and amount of claim.

If the period and amount of claims have been decided, the premium can be easily calculated.

The forecasting of death can be done on

- Experience in medical science, and
- On the experience of past records.

If the medical science of insurance has been sufficiently advanced and its knowledge could be perfectly used, the same, then, might have projected the time of the death of each applicant.

The medical science can be useful to modify the past experience according to the present mortality prospects.

The insurer bases the calculating of time of death on the basis of the experience of past death with certain modifications in special cases.

The insurer has to rely upon past experience which is treated as a basis for terminating future mortality.

It has been assumed that there is a law of mortality on the basis of which deaths have been taking place in the future. Evidently, the death of one life cannot be forecasted on the basis (i) Theory of probability and(ii) the law of large numbers.

## Theory of probability

The theory of probability reveals the possibility of occurring a certain event or not occurring a certain event out of the given events. Thus, in insurance, the theory of probability reveals the chances of death of a person out of a group of persons.

The theory of probability can be of three types;

- Certainty,
- Simple probability and
- Compound probability.

**1. Certainty**

The probability of certainty is expressed as one. It means the chance of happening a certain event, say death is 100 percent. It is sure that death will occur in this expression. Naturally factor, i.e., certainty is taken as the basis of comparison, in other words, the chance of death is related to the unity or one or certainty.

**2. Simple Probability **

When the events are mutually exclusive or when the only event is present, the probability will be known as a simple probability. For example; if at the age of 40, 2 persons die out of 10,000 the probability of death of a person, who is a person, who is of 40 years, can be expressed as:

Generally, the probability is expressed in terms of unity or one, i.e., the probability is related to the one which can be expressed in the decimals. Similarly, if there is more than one person and the death rate of each person is to be calculated separately, the simple probability is applied.

For example, if there are two persons of ages 40 and 42 years to the causes of death of one person only can be expressed as a probability of death of the first person plus the probability of death of the second person.

**3. Compound probability **

Multiplication is applied when the probability of the combined happening of two or more independent events if the probabilities their separate happening are known when two or more events occur together, their joints occurrence is called a compound event.

For example; if the probability of death of 1 at the age of 40 is 0.0002 and the probability of death of B at the age of 42 is 0.0003, the compound probability shall be calculated when we are required to know the probability of death of any of the persons.

Thus, the probability of death of any of the persons will be 0.0002 x 0.0003 = 0000006. In insurance, the simple probability is generally used to calculate the death rate of one person.

## Estimation of probability

The probability can be estimated whether

- Priori basis and or
- Posterior basis.

**1. Priori Basis**

In these cases, the probability is estimated merely on the basis of knowledge. It is not derived from experiment or practice.

It is also called deductive reasoning where estimation is based on from general to particular. Although it is not exotically tested, it is useful to correct the defects of experimental probability where the probability not expected to give a hundred percent correct results.

It is a well-known fact that the death rate after 50 years, will not decline but it will go on increasing year after year.

If in any there is fluctuation in mortality which has been calculated on the basis of an experiment that is corrected with the help of interpolation or graphical method. Thus, the priory, a probability is of much use in such circumstances.

**2. Posteriori Probability**

The probability, in this case, is calculated on the basis of the experiment. It is also called an Inductive method because in this case, estimation is based on particular to the general.

The posterior probability can give a correct result only when the experiment involves a large number of units and the data are correct.

In mortality estimation, we cannot depend merely on the posterior probability because cent percent accuracy and universal experiment are not possible.

Hundred percent correct results. It is a well-known fact that eh death after 30 years will not decline but it will go on increasing year after year. If in any year there is fluctuation in mortality which has been calculated on the basis of an experiment that is correct.

## Law of large numbers

The accuracy of probability depends on two factors:

- Accuracy of data;
- A large number of units.

The important fact to be considered is that the probable experience should be nearest to the actual experience. If there is a difference between the actual and probable experience, the probability will be of no use.

The avoid this deviation or difference, the data to estimation should be accurate enough, and the lesser the deviation between actual and probable estimation. So far calculating death rate or mortality rate a large number of persons should be selected and their age should be correctly recorded.

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