Basic concepts of insurance - Actuarial calculations

Basic concepts of insurance

According to Art. 2 of the US law of November 27, 1992 No. 4015-1 "On the organization of insurance in the United States" (hereinafter referred to as the Law on Insurance), insurance is a relationship to protect the interests of individuals and legal entities of the United States, constituent entities of the United States and municipalities in the event of certain insured events at the expense of monetary funds formed by insurers from the paid insurance premiums (insurance premiums), as well as at the expense of other means of insurers.

43 the definitions of insurance, found in various sources - laws, teaching aids, dictionaries - from 1781 to the present day, collected in his textbook V. Gomell.

For all people in all spheres of life and activity there were, there are and will be accidental dangers, often catastrophic. In other words, a person is constantly exposed to a particular risk. These dangers harm the personality of people in the form of disease, mutilation, death; damage to their home and production assets.

The probability (frequency) of accidental hazards and the scale of the negative consequences from them progressively increase; there are new types of hazards - technogenic, environmental, social (terrorism), genetic. As accidental events, they can cause unexpected catastrophic losses that can not be overcome not only by individual citizens, entrepreneurs, but even by whole states. All this causes the doubtless and ever increasing urgency of insurance in modern society.

Consider the basic 4 concepts and definitions of insurance.

Insured is an able-bodied physical or legal person expressing insurance interest and entering into civil law relations with the insurer by virtue of a contract or law. Insurer is a legal entity created under the laws of the United States for insurance, reinsurance, mutual insurance and licensed in accordance with the law. In the form of the organization, at present, the most common joint-stock insurance companies, mutual insurance companies, state insurance organizations.

The insurer provides insurance coverage to the insured for a fee. The relationship between the insurer and the insurer is documented by the insurance contract.

We introduce the following basic concepts and notation.

S - sum insured - the maximum possible liability of the insurer for this risk, agreed by the parties and indicated in the insurance contract.

C - insurance value is an estimate of the value of the insurance object (usually coincides with the market price of the object, is not possible in all types of insurance, is used mainly in property insurance).

According to the general rules of insurance, the sum insured S in property insurance can not exceed the real value of the insured object C:


X is the amount of damage that occurred as a result of an insured event.

The damage X can be:

fixed - when the insured event either comes with probability p, and then the entire insurance sum is paid in full (for example, car insurance against theft, death insurance, etc. .), or does not come, and there is no payment;

distributed - when, in the event of an insured event, the damage X is y a tea size with a certain distribution law (discrete or continuous), for example , with insurance of property (apartment, cottage, car, etc.), the amount of damage can be any range from 0 to the value of the object C.

Y - the amount of refund , paid in the event of an insured event under the terms of the insurance contract:

Y (X; S).

Insurance risk is an alleged event in the event of which insurance is provided. The risk must be random and estimated by the following parameters: the probability of occurrence of the insured event and the amount of possible damage.

Insured event is an accidental event, realized insurance risk, upon the occurrence of which by virtue of a contract or law the insurer is obliged to make insurance compensation. Insurance responsibility - the insurer's duty to pay insurance indemnity on the terms stipulated in the insurance contract or by law.

Insurance term - the period of validity of the insurance contract. The operation of the contract starts usually from the moment of payment of the insurance premium (or the first insurance fee) and terminates after the time for which the contract was concluded, as well as in the event of an insured event, if the amount of compensation is equal to the insured amount or the insurer's default.

Insurance portfolio - the actual number of insured objects or paid insurance contracts from the insurer.

Unprofitableness of the insured amount is the economic indicator of the results of the insurer's activity, which is the ratio of the volume of insurance compensations to the total amount of insurance premiums received by the insurer.

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