• Net premium - part of the insurance premium intended directly to cover the damage. The net premium is the main component of the gross premium.

  The net premium consists of the net net risk premium and the risk (insurance) premium.

Related concepts

Interest income - income received by the owner of funds from providing them for a while to other economic entities. Represents compensation paid for the use of financial resources. It is usually expressed as an annual percentage rate.

Statement of cash flows - a company's report on the sources of funds and their use in the reporting period, directly or indirectly reflecting the company's cash receipts, classified by main sources, and its cash payments, classified by main directions of use during the period. The report gives an overall picture of operating results, short-term liquidity, long-term creditworthiness and makes it easier to conduct a company's financial analysis.

Interest rate risk or interest rate risk is the risk (possibility) of financial losses (losses) due to unfavorable changes in interest rates. Interest risk may be due to a mismatch in the terms of demand (repayment) of claims and obligations, as well as a unequal degree of change in interest rates on claims and obligations.

A risk measure is a function that allows you to obtain an assessment of the financial risk for a certain portfolio of assets in quantitative terms (most often in monetary terms). The measure of risk is used to determine the amount of reserve capital required to meet the requirements of the regulator.

Mezzanine loan (eng. Mezzanine Loan) - a relatively large loan, as a rule, unsecured (i.e. provided without collateral of property) or having a deeply subordinated security structure (for example, a lien on property of the third priority, but without the right of recourse in relation to borrower). The repayment period of the loan usually exceeds five years, with the principal repaid at the end of the loan term. As part of a standard offer, the loan is accompanied by a tear-off certificate (coupon), giving the right to...

Costs - the amount of resources (to simplify, measured in monetary terms) used in the process of economic activity for a certain period of time. Or in simple terms: costs are the valuation of resources.

Mortgage insurance (eng. Mortgage insurance) is insurance against the risk of losses from creditors that may arise in the event of defaults of mortgage borrowers and the subsequent sale of the pledged property (lack of funds from the sale of the pledged property and the inability to recover the balance from the borrower).

Accident insurance is a type of personal insurance. Intended to compensate for damage caused by loss of health or death of the insured.

The (zero-coupon) yield curve or term structure of interest rates is the dependence (dependence curve) of the yield of homogeneous financial instruments on their terms (duration). The base yield curve is built on government securities (G-curve, G-Curve) of various maturities (in Russia - on OFZ). You can also build your own yield curve for a specific organization based on the cost of attracted resources, depending on...

Income tax - a direct tax levied on the profits of an organization (enterprise, bank, insurance company, etc.). Profit for the purposes of this tax is generally defined as the income from the activities of the company minus the amount of established deductions and discounts (however, it is never less than 12.5%). Deductions include ...

Net national product (NNP) - the total volume of goods and services that a country produced and consumed in all sectors of its national economy over a certain period of time.

Full cost of the loan (FCC) - the borrower's payments under the loan agreement, the amounts and terms of payment of which are known at the time of its conclusion, including taking into account payments in favor of third parties specified in the agreement, if the borrower's obligation for such payments follows from the terms of the agreement. The total cost of the loan is calculated as an annual percentage.

The weighted average cost of capital (WACC) is the average interest rate across all of a company's funding sources. The calculation takes into account the share of each source of financing in the total cost.

Coinsurance (eng. coinsurance) - joint insurance by several insurers of the same object. This method of providing insurance protection is used, as a rule, when insuring large objects, when one insurance company is not able to take on large risks.

Financial mathematics is a branch of applied mathematics dealing with mathematical problems related to financial calculations. In financial mathematics, any financial instrument is considered from the point of view of some (possibly random) cash flow generated by this instrument.

Tail risk or residual risk is the risk that the price of an asset or portfolio of assets will change by more than three standard deviations from the current price. However, most asset managers control only the risk of loss, that is, the risk of a price drop of more than three standard deviations below the current price.

Bank liquidity is the bank's ability to ensure timely and complete fulfillment of its obligations.

Insurance risk is an event, the occurrence of which is not defined in time and space, independent of the will of a person, dangerous and, as a result, creating an incentive for insurance; this is the risk that can be assessed in terms of the probability of an insured event and the amount of possible damage.

The minimum acceptable rate of return (MARR) is the minimum rate of return on a project that a manager or company is willing to accept before starting a project, given its risk and the opportunity cost of other projects in the business and engineering. A synonym seen in many contexts is the minimum attractive rate of return.

The Internal Measurement Approach (IMA) is one of the advanced approaches (AMA) to operational risk assessment proposed by the Basel Committee on Banking Supervision. The approach is based on supervisory approved gamma ratios to translate expected operating losses into capital requirements. - compensation paid to the heads of a joint-stock company in the event of their dismissal or resignation on their own initiative as a result of the takeover of this company by another or a change in ownership. Used as a counter to a hostile takeover. The type, amount and procedure for receiving compensation is determined by the employment contract, as well as the company's regulatory documents. The size of a golden parachute in Russia can reach hundreds of millions of rubles.

The internal rate of return (eng. internal rate of return, generally accepted abbreviation - IRR (IRR)) is the interest rate at which the net present value (net present value - NPV) is equal to 0. NPV is calculated based on the stream of payments discounted to today .

Property insurance is a type of insurance in which the object of insurance is a property interest related to the possession, use and disposal of property. It is carried out mainly in the form of voluntary insurance, with the exception of insurance of state property leased. The insurers are any enterprises and organizations of various organizational and legal forms, as well as individuals.

Economic profit is the profit remaining for the enterprise after deducting all costs, including the opportunity cost of distributing the owner's capital. In the case of a negative value of economic profit, the option of leaving the enterprise from the market is considered.

Casco (from Spanish casco helmet or Dutch casco case) - insurance of means of transport (cars, ships, aircraft, wagons) against damage, theft or theft. It does not include insurance of transported property (cargo, English cargo), liability to third parties, etc. Casco insurance actively uses various types of franchise, often the insurance rules provide for the possibility of abandonment.

Double insurance (multiple insurance) - simultaneous insurance of the same property interest, the same object and risk with different insurers, in which the total liability limit of the insurers (the total sum insured under all contracts) exceeds the insurance value ...

Pricing for research and development work (R&D) - setting the price for research, theoretical and experimental work performed with the aim of creating new technology.

n-year mixed life insurance

Net premium is calculated by the formula:

Full life insurance deferred for T years

In this type of insurance, the net premium is calculated by the formula:

n-year term life insurance deferred for T years

Full life insurance with continuously increasing benefits

19. Calculation of net premiums for full life insurance with insurance benefits paid at the end of the last year of life.

CALCULATION OF NET PREMIUM FOR BASIC DISCRETE

TYPES OF INSURANCE

Based on the definition of discrete types of insurance, and the concept of actuarial value, the following formulas can be obtained for calculating net premiums:

1. Full life insurance with insurance benefit payment at the end of the last year of life.

Net premium is calculated as

is a discrete analysis of a continuous simplifying function.

20. Calculation of net premiums for n-year temporary and mixed life insurance with

payment of an insurance benefit at the end of the last year of life.

P-summer term life insurance with benefit payment at the end of the year of death

3. P-summer mixed life insurance with benefit payment at the end of the year of death

4. Full life insurance with payment of insurance benefits at the end of the last year of life, deferred for t years

5. Full life insurance with an annual increase in benefits and payment of benefits at the end of the last year of life

Denoting , we can write in the form

Here, is a discrete simplifying function.

21. Relationship between continuous and discrete types of life insurance.

Discrete life insurance - the sum insured is paid at the end of the year of death. Calculations can be made directly from life tables.

Having calculated the net premiums for discrete life insurance, it is possible to calculate the net premiums for the corresponding types of continuous insurance. In order to connect continuous and discrete types of insurance, it is necessary to make certain assumptions about the distribution of life time for fractional ages.

It is usually assumed that this law is uniform. It is known that in this case the random variables and are independent and have a uniform distribution on . Then we can obtain the following formulas connecting net premiums for the corresponding continuous and discrete types of insurance:

The above formulas make it possible to calculate one-time net premiums for continuous types of insurance through the characteristics , , , which are quite simply calculated from the data given in the general tables of life expectancy.

22. .Analysis of the total claim in the model of long-term life insurance.

Let at the moment of time the insurance company has concluded life insurance contracts. Let us designate through - premiums, and through - the value of the insurance benefit paid under the -th contract at a random moment of time . Arrange the values ​​in ascending order: . Then, at a point in time, the capital of the company can be calculated as

and the company will not go bankrupt if the following condition is met:

where is the current cost of payment under the -th insurance contract. The probability of non-ruin will be calculated by the formula:

which is similar to the corresponding formula for short-term life insurance. That is, the calculation of the probability of non-ruin in long-term insurance is carried out in the same way as in short-term insurance with loss values.

Then the insurance premium will look like:

where is the net premium under the -th contract, and is the corresponding insurance premium, which is calculated similarly to short-term life insurance.

In the simplest case, when the insurance premium is divided in proportion to mathematical expectations, we get:

With more complex models of long-term insurance, it is not always possible to express:

a) the probability of non-ruin in the form of a simple formula of the form (32);

b) net premiums and insurance premiums in the form (34).

Net premium

The premium directed to the formation of the insurance fund, from which insurance payments are made, in domestic practice is called net premium. It is obtained by adding the risk premium and the risk premium:

If the contract provides for insurance of one object for several insurance risks, then the net premium, as a rule, is determined separately for each of them. For example, motor vehicle hull insurance includes payout obligations in the event of "damage" (damage/destruction) and theft. These two risks are of a different nature. They are characterized by their indicators of the probability of occurrence and the amount of payment. Therefore, the risk premiums, and hence the net premiums for each such risk, must be calculated separately.

The methodology for determining the net premium and its components depends on the type of insurance and the nature of the insurer's obligations. From the point of view of the specifics of calculations, two significantly different areas can be distinguished: risky types of insurance and life insurance. Features of determining the price of insurance for these types are discussed further in the relevant paragraphs.

Load

A correctly calculated net premium ensures the break-even operation of the insurance fund with a given level of security guarantee. However, the insurance fund is formed and managed by the insurance company. This activity requires certain expenses, which are financed, among other things, from the funds paid by the policyholders in the form of contributions. Therefore, another premium is introduced into the structure of the premium, which is called- part of the insurance premium intended to cover the expenses and deductions of the insurance company, other than insurance payments and the costs of settling insured events.

In order to carry out its activities in the creation and management of the insurance fund, the insurance company must first of all ensure its functioning. To do this, it is necessary to purchase or rent premises, provide them with electricity and water supply, pay for the work of employees, purchase office equipment, document forms, stationery, etc. That is, the insurer, like any other enterprise, bears administrative expenses (AHR).

But in addition to the usual costs inherent in any company, the insurance company has specific costs associated with finding and attracting customers, drawing up contracts, etc. These costs are sometimes referred to as acquisition (from English, French. acquisition acquisition, conquest). If the sale of insurance services is carried out through an agent network or independent brokers, then the main part of the acquisition costs is the payment for the services of these intermediaries in the form commission fee. Its size is fixed as a certain percentage of the premium received and depends on the type of insurance (insurance product) and sales channel. The commission is also taken into account in the load and usually makes up the bulk of it. The most "expensive" in terms of acquisition costs are sales through insurance agents and brokers who do not receive wages and work only for a commission. Here it can reach up to 25-30% of contributions. A "cheaper" channel is sales through the company's full-time employees, who receive a relatively small commission in addition to their fixed wages.

In domestic insurance practice, administrative and business expenses and commissions are combined by the concept business expenses.

If the insurance company is a commercial organization (for example, a joint-stock insurance company), then the purpose of its work is to make a profit. It can be formed due to the excess of premiums over payments (technical profit) or as a result of successful investment activities of the company (financial profit) or be formed at the expense of planned deductions. For this, a certain percentage is sometimes provided in the load structure. planned profit (PP).

Thus, the load serves to cover the costs of doing business and to form the planned profit. In turn, the costs of doing business are made up of administrative and business expenses and commission.

Net net premium

Determining the net risk premium has traditionally been the domain of actuarial calculations and insurance mathematics. The net net premium is calculated on the basis of data on losses for the previous period and is the product of the frequency of occurrence of an insured event by the average amount of damage for the entire set of insured events that occurred in the past.

Net risk premium = Damage frequency x Average damage

The frequency of damage is defined as the quotient of the number of damage cases in the observed set divided by the number of observation units included in this set.

The average damage is the quotient of the total damage for the observed period divided by the number of damages in the same period.

Risk (insurance) premium

The risk premium is intended to increase the reliability of insurance protection.

When identifying the patterns of occurrence of damage as a result of random events in the past and determining, on the basis of this past experience, unprofitability in the future, two types of errors are inevitable:

• Misdiagnosis resulting from incomplete information. This is due to the fact that the statistical sample is limited and does not meet the requirements of the law of large numbers.
• Forecast error, which consists in the fact that in the future there will not be a complete coincidence with the circumstances of the previous period, on the basis of which the net risk premium was determined. This may be due to the influence of unaccounted for or changed factors. It has been proven that even with very good information about damages, future damage exceeds its value in half the cases.

In order to guarantee reliable insurance protection, i.e. to increase the probability that the collected money will be enough to pay damages in the future in all cases, a risk (insurance) premium is added to the net net premium.

The value of the risk premium cannot be less than the value of the standard deviation of the loss ratio of the sum insured.

Using the net insurance rate to determine the net premium

The expected value of the net premium can be defined as the product of the sum insured and the net rate. The net rate is a percentage that reflects the probability of loss, calculated on the basis of the ratio of damage to the total sum insured of the insured objects.

The amount of the net premium is determined by the formula:

Net premium = Sum insured x Net rate/100

Notes

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See what "Net premium" is in other dictionaries:

Exist., number of synonyms: 1 net rate (1) ASIS synonym dictionary. V.N. Trishin. 2013 ... Synonym dictionary

NET PREMIUM- gross rate element; is designed to form the insurer's resources for the payment of insurance compensation. The overhead costs of the insurer for doing business are not taken into account in the calculation of the net rate. In the actuarial calculation, net rates are taken into account ... ... Big accounting dictionary

See Insurance rates Glossary of business terms. Akademik.ru. 2001 ... Glossary of business terms

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

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

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

Rice. 1. Gross premium structure

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

Currently, this ratio is changing in the direction of 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, which indicates an increase in the importance of the work of an intermediary in insurance (agent, broker), and to a large extent corresponds to world practice.

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

Rice. 2. Possible net premium structure

The risk contribution is intended to cover the risk for all types of insurance, i.e. it is used for insurance payments in the event of an 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 structure of the net premium - it all depends on the management strategy chosen by the insurer. If its goal is to win the insurance market at the expense of prices lower than 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.

Cumulative (savings) contribution is intended for accumulating the amount paid under the terms of a long-term life insurance contract - in the event that the insured person survives until a certain date (at the risk of survival). The funded 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 life insurance, mixed life insurance, pension insurance (in this case, the Russian classification of types of insurance is used).

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

Risk premium depends on the accepted probability of excess of actual payments over calculated ones. The smaller the given probability of exceeding the actual payments over the calculated ones, the higher the size of the risk premium. The ratio between the risk contribution and the risk premium for different types of insurance may be different.

The amount of the savings contribution depends on the accepted rule of money turnover (simple or compound interest), the amount of the insurance (accumulated) amount paid at the risk of survival, the rate of income promised to the insured 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 funded contributions in the structure of the net premium is determined by the type of insurance - risk wear is practically included in all types of insurance, since it provides for risk coverage, and funded - only in long-term life insurance contracts.

Thus, in case of short-term accident and illness insurance, medical or death insurance, property and liability insurance (risk types of insurance), the structure of the net premium necessarily includes a risk premium and, depending on the chosen management strategy company may or may not include a risk premium.

When insuring pensions (long-term type of life insurance), the structure of the net premium includes a funded 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 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 the inclusion of a risk premium in the net premium disappears - the role of the risk (guarantee) premium is performed by the cumulative contribution.

In table. 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 contribution, risk premium and funded contribution - are the sources of formation of special insurance funds - insurance reserves intended for payments under the terms of the insurance contract.

As already noted, the load is a part of the gross premium intended to cover the costs of doing business and to make a profit from insurance operations (Fig. 3).

Rice. 3. Load structure

The first structural element of the load — business costs- relates to the cost of insurance services, the second element is the planned profit of the insurance company from insurance operations.

The costs of doing business are divided into traditional, which have a place for any kind of business, and specific specific to the insurance industry.

Specific types of costs include commission fees to agents and brokers for intermediary activities in the distribution of insurance products, expenses for preventive (preventive) measures, costs associated, for example, with the initial examination (at the conclusion of the contract), as well as the examination associated with the occurrence of an insured event, etc.

Experience of economically developed countries shows that the share of expenses for preventive measures can be 4-6% of the gross premium, and the share of commissions can be up to 20% of the gross premium.