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"Covering capital "is a term from the traditional actuarial science. It describes the value difference between in the future obligations of the insurer still which can be fulfilled for each year of the insurance process - mostly life or health insurances - and in the future still to receiving contributions (prospektives covering capital) or between in the past received contributions and in the past fulfilled obligations (retrospective covering capital). The mathematical indication of the covering capital at the end yearly of an insured one x-year old with beginning of contract m-ten are: _mV_x.
The traditional actuarial science assigns each insurance year a value for insurance benefits, separately according to kind of the accident (death, experiencing, inability to work etc.). This value determines itself, in which the probability for the entrance of the accident is multiplied by the height of the achievement which can be furnished in accordance with contract. The probability is usually inferred according to the current characteristics, only age and sex, from a table, "from the separating order "(when insurance on death or case of experiencing as dying board designates). Also the probability is considered that the insurance year concerned is at all experienced.
Money stream have different value by the interest effect, if they are due at different times. Since the payments of the individual insurance years take place i.e. in each case at different times, in another insurance year, they must be standardized by off or Aufzinsen on the same time. In the traditional actuarial science a interest rate firm for all points of term of payment, when "computing interest designates ", is used with consideration of the interest interest.
With these values in the traditional actuarial science the need net once contribution is determined as bar value of all values for each insurance year at the beginning of the contract (net once contribution after the equivalence principle), which is mathematical indications: _nE_x. "The n stands "for the running time of the contract. "A mark contribution "means that the insurant pays a only one, unique contribution with beginning of contract for the entire contractual insurance protection. "Net "it means that all expenditures for the insurance enterprise, resulting with the fulfilment of the contract, were ignored. The equivalence principle means that the contribution of the contract was determined exactly according to the calculatory need. However the calculatory need is regularly extremely carefully certain, so that these contributions lead nearly with security to surplus.
The need gross once contribution one receives, in which additionally to the achievements still the expenditures for the insurance enterprise are considered. These are in particular the initial conclusion expenditures and the current expenditures for collection and administration. For this become overall sentences, which uses "cost impacts so mentioned ".
Separating orders, computing interest and cost impacts form the bases of calculation of the traditional actuarial science.
Most contracts do not plan a mark contributions to separate regular contributions thus contributions in "rates ", since these a mark contributions are too high, in order to be at one time applied. The traditional actuarial science considers these "rates "- contributions ("current contributions "mentioned) as annuities. Shorter payment of dues periods, monthly contributions, are not e.g. considered in the traditional actuarial science but are determined by simply dividing of the annuity by 12 and beginning of an overall rate addition. The current contributions lead the designation: _nB_x. The computation takes place through "Verrentung "of the a mark contribution. The computation is exactly the same, as if the insurer would grant to the insurant a loan over the a mark contribution and the current contributions is the repayments of this loan. Since however the number of deaths is along-considered at the same time, i.e. with death the loan will issue, arises a pension formula. Thus the annuity is divided equal the a mark contribution by the pension bar value.
At all the traditional actuarial science operates an intensive "recycling "from formulas. Based on the bases of calculation "Kommutationswerte so mentioned is determined ". These are in tables "stored "arithmetic operations. The traditional actuarial science was developed for a long time before the invention of calculating machines (in 17. and 18. Century). The number of the particulars, at that time arithmetic operations of only one contract with running time of 20 years, which can be implemented described above by hand, amounts to several hundreds. Since one has apart from the insured sum only very few parameters (age, sex and running time), can one many computations tabulate, mostly values for lifelong contracts. Receives one insured the value for a contract e.g. of 20-year old running time one with beginning then, by taking the table code off of a with lifelong running time from the table code of the with lifelong running time, whereby still one is necessary for interest and probability of survival only two arithmetic operations demanding correction. The difference are exactly the 20 years contract running time between the age of 30 and the age of 50. In the today's time these table computations are however because of the high computing speed of computers hardly still necessary.
The price for this computing simplification is however that the insurance products and also no differentiation for the computing interest must be arranged extraordinarily simple after duration are possible. These simple products are however extraordinarily favorable in the administration, so that they are prevailing until today in Germany.
The calculation method of the traditional actuarial science makes it possible to determine at the time according to covering capital the used bases of calculation. The traditional actuarial science subordinated in principle that the contributions set in the formulas were determined according to the equivalence principle, thus for all computations the same bases of calculation to be used. Then the prospektive covering capital corresponds to the retrospective.
The covering capital can simply as the need once contribution described be able to furnish to become, which was still needed beside the future current contributions, in order the future payments. The formulas for the covering capital are arranged accordingly. Since the computations of the covering capital must be accomplished annually for each contract, the formulas became particularly efficient, i.e. arranges with as few an arithmetic operations by intensive use from values as possible already tabulated. The traditional actuarial science was developed in particular for the efficient annual computation of the covering capital for the purpose of the determination of the covering resetting.
The traditional actuarial science was developed for a world without computers. Their principal purpose direction is the minimization of the number of arithmetic operations. For this substantial restrictions were taken with the accuracy of the calculation and with the flexibility of the products in purchase.
It is to be hardly still justified with the today's requirements at accuracy that in one month due payments with the same interest as in are abgezinst 10 years due payments, instead of using an interest structure curve.
Abroad, where the method of the traditional actuarial science is called "deterministic method ", already substantially more flexible, procedures making of the possibilities of the modern computer engineering use are usually, e.g. "the stochastic "or "analytic "methods. The products developed thereby cannot be illustrated with the methods of the traditional actuarial science any longer. For such products neither bases of calculation nor covering capital are assignable in the traditional sense.
On the other hand the products determined with the traditional actuarial science represent today still the simplest, concomitantly most transparent and most efficient products, which give it. As soon as however contract purpose is not any longer alone the risk security and the supply of a certain capital (or pension) when experiencing, but a financial speculation on market values in capital markets is desired, is overtaxed these methods.
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