Conversion of extra risks into special insurance conditions in the life insurance

In this paper we will describe the application of mathematic methods in the conversion of extra risk into the special insurance conditions in the life insurance. The main fields of risks and uncertainties in the life insurance company are: mortality and sickness, investment gain, taxation and inflation and new products of life insurance company. We will deal mainly with the risks connected with mortality. Life Insurance Company is exposed mainly to these risks that arc for it the main and typical risks. The size and importance of the mortality risk depends mainly on the product type. From this point of view we can divide the life insurance products into the two types. The so-called risk insurance (for instance the temporary insurance for the case of death), which are sensitive oil the mortality premises and the so-called reserve-making insurances (for instance the combined insurance - endowment insurance), which Ire not sensitive on the mortality premises but oil the Financial premises, above all on the interest rate (investment gain). One of the most important tools used by the insurance company to reduce the mortality risk is the careful subscription. The insurance company can reduce the mortality risk also by blocking relatively large part of each insurance. Also in this case, however, it is important to subscribe carefully. as covering insurance company does not take over from the insurance company the part of whichever risk. The main demand of this covering insurance company is the subscription process quality. We will deal further above all to the non-standard mortality risks (extra risks) and their conversion into the price of insurance (premium) of such a risk. The insurance companies identify extra risk in the process of subscription. The subscription and the life insurance are defined as the creation and sale of insurance. It consists of the definition of the risk and conditions under which the insurance company takes over this risk as well as of the definition of guarantees and persons who will be given Such guarantees by the insurance company. Thus, before the insurance company insures a certain person, it tries during the subscription process to find out if the standard insurance is adequate to the health state of the relevant person. Most insurance companies accept by 90 to 95% insured standard rates. This percentage varies depending oil whether the insurance company prefers the competition values of premium or large-hearted subscription policy. The size of the group of standard insured persons depends however not only on the competition, but also on the sort of product and oil (lie progress in medicine. Extra risks are the risks where the insurance company applies the use of special conditions. Extra risk related to mortality can be quantitatively expressed in three forms: percentage of normal mortality, addition to age, increased mortality intensity. The insurance company must convert these forms of extra risk quantification into special insurance conditions. Several methods exist. The most important are: extra premium, deduction, exclusion clause, postponed decision, rejection, offer of an alternative contract or the change of original contract. Two methods - extra premium and deduction are exact, e. g. they enable conversion of the extra risk by the quantifiable form. We deal with them in more detail. Extra premium is the supplementary premium by which standard premium is increased. It reflects the character of extra risk and of the contract type. The method of its definition depends on the method of the insurance company in quantifying the extra risk. We can demonstrate how one can model the increase of mortality intensity up to the value mu(x)' = mu(x) + c by the increase of interest rate. To describe the situation we can use the linear methods of insurance mathematics. We will use the above-mentioned modelling for the calculation of the extra premium for basic products of life insurance (pure endowment insurance, temporary anticipated pension, endowment insurance, temporary insurance for the case of death and combined insurance) by means of the standard mortality tables at the increased interest rate. Deduction is the sum the insurance company will deduct from the insurance settlement in case of death. In case of endowment term fulfilment the insurance settlement is unchanged interested person with an extra risk pays the same premium as the one with standard risk, in case of death, however, the insurance settlement is lower. Deduction can be set by two methods. The first one is simple - deduction is constant throughout defined fixed time. At the second method deduction at the insurance start is quite high and decreases to nil as the insurance time progresses. We will evolve the formula defining deduction Z (t) related to the unit of insurance sum in time t in the case of decreasing deduction. At that the first method of risk quantification will be used. We will present also the advantages and disadvantages of the deduction and extra premium as methods of risk conversion into the insurance price.