Johdanto

Työssä käsitellään Yksilöllisen henkivakuutuksen perusteen SHV-tutkintoa varten (1988) sisältöä ja erityisesti laskuperusteessa esitettyjen vakuutusten vakuutusmaksujen ja rahaston laskentaa. Viitataan jatkossa kyseessä olevaan perusteeseen lyhyemmin nimellä SHV-laskuperusteet.

Tavoitteena työssä on luoda selkeä esitys kiinteämaksuisten yksilöllisten henkivakuutusten laskuperusteiden mukaisesta nykyarvon laskennasta. Käytännössä vakuutusmaksujen ja rahaston laskenta tehdään samalla tavalla kaikille vakuutuksille siten, että perusteiden mukaisesti vakuutuksesta aiheutuville tuleville suureille, riskimaksuille ja kuormituksille, lasketaan vakuutustekninen nykyarvo ottaen huomioon korko-oletuksen ja kuolevuuden vaikutus. Suureiden nykyarvoista voidaan laskea niitä vastaava vakuutusmaksu ja määrätä rahaston määrä.

Abstract

The aim of this work is to show the calculation technique of the expected present values and the savings of life insurances with fixed premiums presented in the calculation rules called "SHV-laskuperusteet". These insurance contracts can include pure endowment insurances, insurances for death, and also insurances for short and long term disability. These kind of life insurances with fixed premiums were sold regularly in the past but nowadays insurances with flexible premiums are more common. There still is a significant amount of these "old-fashioned" life insurances in-force.

The calculation rules presented are based on the actual calculation rules which all life insurance companies in Finland had to use in the past. Fixed premiums and reserves are quite easy to calculate using only a few facts of the insured person and also pre-calculated charted values of the expected present values. Fixed premiums can be calculated using the present values of the expected risk premiums (the expected claims) and loadings which are set in the calculation rules. The present values of the expected future risk premiums and loadings minus future premiums can be used as the basis of the technical provision of an insurance contract.

To calculate risk premiums and loadings, intensities like mortality depending on sex and age are used. Using this calculation method we can for example derive probabilities of an insurance event at some time period integrating insurance event intensities over time. Then we can easily calculate the expected present values of the future cash flows needed for the calculation of the premiums. For the calculation of the expected present value we take into consideration only the probability that the insured person lives in the future at time given, and the interest rate set in the calculation rules. This means that future claims and loadings can only occur when the insured person is alive. Naturally the premiums will also end if insured person dies.

General equations for calculation of the expected present values are also included in this work. This is actually the most important point in the work. The same method can be used for all the insurances in this work. The presented general equations use only the continuous intensity of some future quantity as presented in the previous paragraph. Then we calculate the actual expected present values of the insurance claims and loadings for the most of the insurances of the calculation rules.

Using the present values we can also calculate reserves, savings, surrender values, and also the insured sum of an insurance in which the insurance policy holder has cancelled the premium payments.

In the appendix there is also presented the cases of two insured persons in more detail, the actual numerical assumptions, and some basic features of the different insurance types of the calculation rules.

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