Gross premium. See the meaning of Gross premium in other dictionaries

Gross premium or insurance premium, represents the amount of insurance payments under the insurance contract, paid by the insurer to the insurer (insurance organization) for a certain period from the entire insured amount.

The gross premium depends on the amount insured, the degree of risk and the period for which this insurance premium is made. This period may not coincide in duration with the total insurance period. The gross premium structure reflects economic mechanism insurance.

It is possible to highlight two elements — net premium, intended for insurance payments under the terms of the insurance contract, and load, intended to cover the costs of running a business and making a profit from insurance operations (Fig. 1). Note that the net premium calculated per unit of insurance amount, usually equal to 100 rubles, is called net rates.

Rice. 1. Gross premium structure

The ratio of net premium and load depending on the type and volume of insurance, as well as on the level of costs of running a business, may be different.

Currently, this ratio is changing towards increasing the load share to 15-20%, as is customary in world practice. This trend is mainly due to an increase in the structural element of the load - commission remuneration, which indicates the increasing importance of the work of an insurance intermediary (agent, broker), and is largely consistent with world practice.

IN general case the net premium may include the following structural elements — risk contribution, risk (guarantee) premium and savings (savings) contribution(Fig. 2).

Rice. 2. Possible net premium structure

The risk contribution is intended to cover the risk of all types of insurance, i.e. it is used for insurance payments upon the occurrence of insured event. It is always present in the structure of the net premium.

Risk (guarantee or stabilization) premium is intended to compensate for the possible excess of actual payments over the calculated ones taken into account in the form of a risk contribution. This premium may not be included in the net premium structure - it all depends on the management strategy chosen by the insurer. If its goal is to conquer the insurance market due to lower prices compared to other insurers, this element (risk premium) is not included in the net premium structure. If the insurer wants to strengthen its financial stability, this element is included in the net premium.

Accumulative (savings) contribution is intended to accumulate the amount paid under the terms of a long-term life insurance contract - if the insured survives to a certain date (according to the risk of survival). The savings contribution must be invested in order to generate income. It is a structural element of the net premium of long-term life insurance contracts, for example, for survival insurance, mixed life insurance, pension insurance (in this case, the Russian classification of types of insurance is used).

Risk contribution amount in net premium depends on the insured amount and the probability of an insured event.

Risk premium amount depends on the accepted probability of actual payments exceeding estimated ones. The lower the specified probability of actual payments exceeding the calculated ones, the higher the size of the risk premium. The relationship between the risk premium and the risk premium for different types of insurance may be different.

Savings contribution amount depends on the accepted rule of money turnover (simple or compound interest), the size of the insurance (accumulated) amount paid for the risk of survival, the rate of return promised to the policyholder and the duration of the contract (accumulation period). For a funded type of insurance, the ratio of risk and funded contributions is determined by the terms of the contract.

The inclusion of risk and accumulative contributions in the structure of the net premium is determined by the type of insurance - risk depreciation is practically included in all types of insurance, since it provides for risk coverage, and accumulative - only in long-term life insurance contracts.

So, with short-term insurance against accident and illness, health insurance or death insurance, when insuring property and liability (risk types of insurance), the net premium structure necessarily includes a risk premium and, depending on the chosen company management strategy, may or may not include a risk premium.

When insuring a pension (long-term type of life insurance), the net premium structure includes savings contribution, which is intended for payments to the insured at the risk of surviving until a certain date, for example, until the date of the next payment. Note that for long-term life insurance contracts, which simultaneously provide for both risk coverage (the risk of death and, perhaps, the risk of an accident) and the accumulation of funds in case of survival, for example, for mixed life insurance contracts, the need for When the risk premium is included in the net premium, the role of the risk (guarantee) premium is played by the savings contribution.

In table 1 presents options for possible gross premium structures for various types of insurance.

Table 1

Gross premium structure options for different types of insurance

Net premium elements- risk premium, risk premium and savings contribution - are the sources of the formation of special insurance funds - insurance reserves intended for payments under the terms of the insurance contract.

As already noted, the load represents the part of the gross premium intended to cover the costs of running the business and to generate profit from insurance operations (Fig. 3).

Rice. 3. Load structure

First structural load element — business costs- refers to the cost of insurance services, the second element is the planned profit of the insurance organization from insurance operations.

The costs of running a business are divided into traditional, which take place for any type of business, and specific, characteristic specifically for the insurance business.

Specific types of costs include commissions to agents and brokers for intermediary activities in the distribution of insurance products, expenses for carrying out preventive measures, costs associated, for example, with conducting an initial examination (when concluding a contract), as well as examination associated with the occurrence of an insured event, etc.

Economic experience developed countries shows that the share of costs for carrying out preventive measures can be 4-6% of the gross premium, and the share of commissions can reach up to 20% of the gross premium.

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Calculation of gross premium

The gross premium is calculated based on the gross insurance rate. The gross rate consists of the net rate and the load on the net rate.

Net rate

The net rate is intended to form an insurance fund in its main part, which is intended for insurance payments in the form of insurance compensation and insurance coverage. The net rate is calculated based on the probability of damage to the policyholders. If the terms of the insurance contract provide for several types of insurance liability, then the total net rate may consist of the sum of several private net rates.

Business expenses represent (by analogy with production activities) the cost of insurance operations and include the following expenses:

remuneration of full-time and non-staff employees of the insurance organization;
rental of premises;
payment for electricity, heating, water supply, postal, telegraph, telephone costs;
travel expenses;
other expenses of the company associated with its activities.

Net rate calculation

Most important for correct calculation insurance rate has a justification for the net rate. It is its correct definition that guarantees the financial stability of the insurer. However, calculating the net rate is the most difficult moment when determining the insurance rate.

The probability of the occurrence of an insured event is determined a posteriori, i.e. based on past experience. IN classical theory The net rate, calculated as a percentage, is the probability of the occurrence of an insured event. For example, if out of one hundred objects with the same value accepted for insurance, on average one object dies during the insurance period, then the probability of such an event occurring or, accordingly, the probability of losses is equal to one percent. Therefore, in order to create an insurance fund intended to compensate for losses, Insurance Company must set the net insurance rate at one percent of the insured amount. The relationship between the amount insurance compensation, paid for a certain period, and the total insured amount of all insured objects is called the loss ratio of the insured amount. It is this indicator that underlies the calculation of the net rate for the so-called risk types of insurance, i.e. types of insurance not related to long-term life insurance.

Having calculated the average loss ratio of the insured amount for a number of years based on observational data, the insurance company then uses mathematical statistical methods to assess the stability of this indicator. If the dynamic series is sufficiently stable, then the basis for calculating the net rate is the average loss ratio of the insured amount, to which is added a risk premium equal to at least the standard deviation. With this determination of the net rate, it can be stated with a probability of 84% that the loss ratio of the insured amount will not exceed this calculated value. If you add the double value of the standard deviation to the average loss ratio of the insured amount, then the probability that the loss ratio of the insured amount will not exceed this value increases to 98%.

Final formation of the insurance tariff

Having thus determined the value of the net rate, the load is added to it and the size of the insurance tariff is determined. The insurance rate is determined on the basis of special mathematical calculations, which are called actuarial calculations.

Notes

Literature

Kazantsev S.K. Insurance Basics: Tutorial. - Ekaterinburg: ed. IPK USTU, 1998 ISBN 5-8096-0006-9

Calculation of net rates for risk types of insurance

Definition 2

The net rate is an indicator equal to the net premium calculated per unit (usually 100 rubles) of the insurance amount.

The methodology for calculating the net rate for risky types of insurance implies the availability of a sufficient amount of statistical data necessary for making accurate calculations, the conclusion of a large number of contracts (for the same period) is predicted, and it is also assumed that there are no events that could lead to payments immediately several insurance cases.

In accordance with the methodology, the formula for calculating the net rate $Tn$ has the form:

$Tn = To + Tr$, where:

$To$ – risk premium (part) of the net bet,

$Tr$ – risk premium.

The risk premium is calculated as follows:

$To = Q Sb ⁄ S 100$, where:

$Q$ is the probability with which the occurrence of an insured event is possible,

$Sb$ – average amount of insurance payment,

$S$ is the average amount of the insured amount.

$Q = M ⁄ N$, where:

$M$ – number of insurance events that occurred,

$N$ is the number of contracts concluded over a certain period of time.

The average amount of insurance payment is equal to the ratio of the amount of payments for all contracts to the number of contracts:

$Sb = (∑Sbi) ⁄ M$

The average amount of the insured amount is equal to the ratio of the total amount of insured amounts for all contracts to the number of these contracts:

$S = (∑Si) ⁄ N$

The risk premium $Tr$ is equal to:

$Tr = Then α(γ) √ ((1 – Q + (Rb ⁄ Sb)^2) / (N Q))$, where:

$Rb$ – standard deviation of the average insurance payment,

$α(γ)$ is a coefficient that depends on the probability γ chosen by the insurance company that the premiums will be enough to cover the damage. The value is taken from the table:

Figure 1. Coefficient values. Author24 - online exchange of student work

Calculation of net rate for life insurance

The main factors influencing the size of the net rate for life insurance include:

age and gender of the insured person;
duration of the contract and procedure for payment of contributions;
the projected return on funds received by the life insurance reserve fund if they are invested.

The calculation of the net rate is based on data from tables on the mortality of the population of a certain age and average life expectancy.

To begin with, the necessary indicators are calculated

The probability of death in a given year of life $Qx$ is calculated by the formula:

$Qx = Bx ⁄ Lx$, where:

$Bx$ is the number of people who die in the period from $x$ to $x + 1$ years,

$Lx$ is the total number of people who lived to be x years old;

The probability with which a person will live to a given age, $Px$, is equal to:

$Px = L(x+1) ⁄ Lx$, or:

Taking into account the fact that contracts for this type of insurance have a long period of validity, and funds received from the policyholder can be used by the insurance company for investment in order to receive additional income, to adjust the final net rate, use a multiplier $V^n$ equal to:

$V_n = 1 ⁄ (1+i)_n$, where:

$i$ – rate of return from investment,

$n$ – number of years for which funds are invested.

As a result, the size of the net premium $(Ex)_n$ for survival will be equal to:

$(Ex)_n = (L(x+n) V_n) / Lx S$, where:

$L(x+n)$ – the number of people who survived until the end of the period for which the contract was concluded,

$n$ – the period for which the contract was concluded,

$S$ is the amount of the insured amount.

The net bet on the possibility of death $(Az)_n$ is equal to:

$(Az)_n = (Bx ∙ V + B(x+1) ∙ V_2 + ⋯ +B (x+n-1) ∙ V_n) / Lx ∙ 100$, where:

$Bx, B(x+1)…B(x+n-1)$ – the number of people dying in the period from $x$ years to $x+1$, calculated for each year of the contract period.

When concluding a combined insurance contract for both survival and the possibility of death, the net rate will be equal to:

$Тн = (Ex)_n + (Az)_n$

This method of calculating the net rate is applicable provided that the entire amount insurance payment is paid immediately during the insurance period. If the policyholder wishes to divide the premium amount into several parts equal to the number of years of insurance, then the amount of the annual payment $P^x$ will be equal to:

$Р_x = (Ed)_x / α_x$, where:

$(Ed)_x$ – size of the calculated one-time payment,

$α_х$ – installment coefficient, which represents the cost of payments in the amount of one monetary unit. In fact, this indicator is close in magnitude to the value of the number of years for which the contract is concluded, but is slightly lower than it. As a result, the amount of annual payments exceeds the value equal to simply dividing the lump sum contribution by the number of years of insurance. In this case, the insurer compensates for the losses it incurs from the inability to invest the entire amount at once and receive income from it.

Gross premium is the total amount insurance premium, which the policyholder pays to the insurer under the insurance agreement. In other words, it is the sum of all premiums associated with insurance. It is calculated taking into account the costs of concluding an agreement, supporting the case, the insurance itself and its extension.

What elements does it consist of?

The gross rate is the basis for calculation. Its components are the net rate and load. A net rate is applied to establish the base insurance fund intended for payment of compensation. Its size is directly dependent on the likelihood of possible damage to the insurance object. If the insurance contract provides for several forms of liability for the insurer, then the total net rate may consist of several parts.

Typically, the load on the net rate is the smallest element of the gross rate. But often its size becomes quite impressive for specific forms of insurance contracts. It includes such types of expenses that differ in their purpose, such as deductions for the maintenance of the insurance business and management, the profit of the insurer, and the costs of preventive measures. The costs of running an insurance business are expressed in the cost of insurance operations and are divided into the following types:

Costs for concluding and renewing insurance contracts, namely:
- payment of remuneration to agents, most often in the form of a commission;
- wages for employees drawing up contracts;
- costs of maintaining call centers;
- advertising and marketing expenses.
Payments for electricity, heating, water, postal and telephone costs;
Rental payments for premises;
Payments to posted workers;
Other expenses of the organization related to the implementation of activities.

Correct calculation of the net rate guarantees stable financial position insurance company. The possibility of a risk event occurring is calculated based on an analysis of past events and the frequency of their occurrence. So, if out of 100 identical in cost residential buildings over a certain period, 5 will be destroyed, then the coefficient of the probable occurrence of such an event will be equal to 5%. This means that in order to correctly form an insurance fund for compensation of losses, the company needs to set a net tariff rate of 5% of the total insured amount.

How is the calculation carried out?

Example of gross premium calculation

Insurance organization provides insurance for citizens against accidents. Using special calculations, it was found that the average sum insured- 300,000 rubles, security - 200,000 rubles, average range of compensation - 55,000 rubles, guaranteed safety coefficient is 0.98, number of concluded contracts - 5,000, number of risk situations in them - 400, share of load to net rate - 25 %. It is necessary to calculate the gross premium and its components. The probability of an insurance situation occurring is calculated using the formula:

where is the probability indicator; - number of cases; - the total number of contracts. That is, the probability indicator is 400 / 5000 = 0.08. The main part of the net bet is calculated using the formula:

where is the base part; - average support; - average value of the sum insured; - risk probability coefficient. That is, the base part is equal to 200,000 / 300,000 x 0.08 x 100% = 5.36 rubles. The size of the guaranteed premium to the net rate is calculated using the formula:

where is the guaranteed risk premium; - basic part of the net rate; - indicator of the probability of risk occurrence; - safety guarantee factor; - total number of contracts. After substituting the available data into the formula, it turns out that the guaranteed risk premium is equal to 0.1. The total net rate is determined by the formula:

where is the total net rate, and the remaining arguments are known. Thus, the net rate is 5.36 + 0.1 = 5.46 rubles. The gross rate is calculated as follows:

where is the gross rate; - interest load. That is, the gross rate is (100 x 5.46) / (100 - 25) = 7.28%. Having all the data, you can calculate the gross premium:

where is the gross premium; - maximum amount insurance coverage; - gross rate. Then the gross premium will be equal to 300,000 x 7.28% = 21,840 rubles.

Calculations have shown that the cost of accident insurance for citizens should not exceed 21,840 rubles. The client package may include such types of services as insurance protection from disability, injury, death. It is possible to fix the price of the specified package for a period of up to 1 year. This measure helps improve the quality of insurance coverage, the availability of medicine and medical care for injuries (particular emphasis on sports injuries), reducing the number of relapses, improving treatment results under conditions of regular monitoring, and so on.

Conclusion

Thus, the gross premium is the final amount of the premium that is paid to the insurer under the insurance contract and takes into account all components of the price of the insurance service. Most often, to calculate the premium, you need to know statistical data for the previous period, since the main components of the formula are indicators such as net premium and load.