Actuarial reserve

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Premium reserve , often abbreviated as DRS, is a term used in accounting . He refers to the balance sheet of an insurer scheduled value of the obligation arising from a life insurance contract or any other contract with long lasting coverage. The actuarial reserves of the contracts form the most important debt item on the liabilities side of the life and health insurers and belong to the technical reserves . The provisions on solvency ( capital adequacy ) and the amount of capital investments to be held as insolvency protection in the guarantee assets also refer to the actuarial reserve determined for commercial law purposes . The contractual regulations for determining the profit share usually determine the actuarial reserve as the assessment basis.

Concept of the actuarial reserve

The term “actuarial reserve” relates to the value to be formed for the individual contract. However, the total item in the balance sheet, i.e. the sum of the actuarial reserves for all contracts, is often referred to as the actuarial reserve for short but imprecisely. The value for the individual contract is then called - just as imprecise - cover capital , which actually describes every actuarial determination of a contract value . In the older literature, in particular, one can also find the terms “reserve”, “premium reserve” or “balance reserve”. However, the actuarial reserve is a provision and not a reserve in the sense of accounting.

Function of the actuarial reserve

The mathematical provision describes the commercial law to be applied in amount of the liability of the insurer under the obligations under an insurance contract, as far as it does not affect already due or due to already occurred insurance claims relate existing claims. As these obligations are uncertain, it is a provision. The debt consists in the insurer's backlog of performance from the contract for which the policyholder has already paid contributions in fulfillment of his contractual obligations , but the insurer has not yet fulfilled his consideration, the insurance cover or the provision of other services. Such a performance arrears must be taken into account in order to present an asset, financial and earnings position that corresponds to the actual circumstances, even if the obligation may not become due for decades. With their premium payments, which the insurer has shown as income, the policyholders have acquired claims that the insurer has to show in return. When assessing the future obligations of the insurer, those contributions by the policyholder that the policyholder still has to make in order to maintain the claim are taken into account.

The actuarial reserve also has an important function in safeguarding the interests of policyholders. The actuarial reserve determines the amount of assets that the insurer must hold in order to ensure that the contracts can be continuously fulfilled. At the same time this power is provided as a backup capability with a bankruptcy privilege provided the policyholder, so that these are preferably in the event of bankruptcy, the capacity can be obtained which corresponds to the value of their claims for the particular contract.

Legal regulations

In addition to the general provisions of commercial law in § 246 HGB, in particular the requirement of completeness, and § 252 HGB, in particular the individual valuation principle , the principle of prudence , the imparity principle , the realization principle and the continuity requirement, and the general provisions of § 341e HGB that apply to technical provisions the provisions on the recognition and valuation of the actuarial reserve in Section 341f of the Commercial Code (HGB) and further provisions in Section 25 and Section 32 RechVersV or in Section 13 and Section 17 RechPensV . According to Section 341e, Paragraph 1, Clause 2 of the German Commercial Code (HGB), the provisions of insurance supervisory law on the minimum level of caution to be applied when choosing the calculation basis for the actuarial reserve must also be taken into account. The regulatory norm can be found in Section 65 of the Insurance Supervision Act (VAG), or in Section 116 VAG for pension funds , and in the statutory ordinances issued for this purpose, the Insurance Reserve Ordinance ( DeckRV) for life insurance, the Calculation Ordinance (KalV) for health insurance and the Pension Fund Premium Reserve Ordinance (PFDeckRV, repealed with effect from July 1, 2016) for pension funds.

The German regulations are based on European law ( Directive 2002/83 / EC ). The corresponding regulations of other European countries, such as Austria or Switzerland, are therefore not significantly different. In Switzerland, the determination of the actuarial reserve is regulated by Articles 58–65 of the Supervisory Ordinance (ISO). For Austria, the determination of the actuarial reserve is regulated by Sections 81i and k of the VAG Austria.

Special German regulations concern the role of the responsible actuary . The actuary responsible must confirm under the balance sheet that the actuarial reserve has been determined in accordance with the applicable regulations. The Actuarial Ordinance (AktuarV) defines further requirements for the actuary responsible for confirming the actuarial reserve (repealed with effect from January 1, 2016). Another specialty concerns the old stock . Here, the assessment is based on the approved business plan within the limits of Section 341e, Paragraph 1, Clause 2 of the German Commercial Code. Changes to the calculation method or the assumptions used therefore require the approval of the insurance supervisory authority .

Insofar as insurance companies prepare consolidated financial statements or individual financial statements in accordance with IFRS , the provisions of IFRS 4 “Insurance Contracts” must be applied. For most insurers, this results in a continuation of the provisions of German commercial law or US GAAP . The IASB is currently preparing a new version of IFRS 4, which may include a valuation of the actuarial reserve at a current value.

Principles for determining the actuarial reserve

The value of the future obligation cannot be clearly determined due to the random nature of the insurance benefits but also due to the uncertainty of future developments, but must be estimated. This also applies if this value is to be determined close to the market, since such market prices are not observable.

The procedure for estimating the actuarial reserve is described by the "technical calculation bases". These consist of the “calculation method” and the “assumptions” or “parameters” required for it.

Calculation methods

Prospective and retrospective method

According to EU regulations, the actuarial reserve must be calculated using the prospective method. It is determined according to actuarial principles as the difference between the actuarial value of the insurer's obligation and the actuarially determined present value of the contributions to be made by the policyholder (prospective method). “Prospective” here means that only future cash flows are taken into account. The wording "obligation" and "contributions" means that all future cash flows, i.e. the total contractual contributions and the total expenses required for the execution of the contract, including all expenses for insurance operations, must be taken into account (gross premium method) . This gross contribution procedure may only be deviated from if this is necessary under commercial law or if the result is essentially the same.

If it is not possible to use the prospective method (for example, in the case of unit-linked life insurance policies or contracts in which the amount of the performance promise is not absolutely fixed for other reasons), the actuarial reserve consists of the compounded contributions received minus the contractual contributions, if interest has been agreed Withdrawals for risk and operating expenses (retrospective method). While the prospectively determined actuarial reserve aims to keep the funds available to secure the promised future benefits of the insurance company, minus the future contributions, the retrospective method determines the residual value of the amounts previously paid by the customer, on the basis of which the future entitlement to benefits is determined in accordance with the contract.

If the same technical calculation bases are used to calculate the actuarial reserve, i.e. the same method and identical assumptions as were originally used when calculating the contributions, then both methods result in the same value.

Other commercial law requirements

The actuarial reserve must fully cover the obligation (completeness requirement). Additional obligations arising during the course of the contract, for example through the allocation of profit shares that increase the entitlement to insurance benefits (i.e. not the interest-bearing, accumulated ones , cf. § 341f HGB), must also be taken into account.

The actuarial reserve is to be determined individually for each contract (individual valuation principle). Approximation procedures are allowed, but it must be ensured that there is no netting between contracts. This concerns two cases: On the one hand, actuarial reserves can also be mathematically negative because of the difference if the actuarially determined present value of the contributions is higher than the actuarial value of the obligation. Such negative actuarial reserves may not be netted with positive ones. Rather, they are to be set at zero. An exception applies if the actuarial reserve becomes temporarily negative due to the risk development during the term of the contract, as can occur, for example, with occupational disability insurance. On the other hand, profits from contracts that are to be distributed according to the realization principle may not be used to cover losses from other contracts that are to be reported immediately according to the imparity principle.

The actuarial reserve must be determined carefully (principle of caution). However, there are insurance-specific special rules in the RechVersV and the VAG.

If the actuarial reserve is not sufficient according to commercial law criteria, it must be increased immediately to the required amount (imparity principle). A distribution of this effort over time is not permitted.

Profits not yet realized, for example from future contribution payments or future interest profits, must not be anticipated (realization principle). Therefore, the gross contribution procedure specified in Section 341f of the German Commercial Code (HGB) must be modified if the contractual contribution is higher than the required contribution (standard contribution) calculated according to the technical calculation bases of the actuarial reserve. In this case, the contribution to be included in the calculation must be reduced to the arithmetical requirement contribution (requirement contribution method). This occurs when the technical basis for calculating the contributions is more cautious than that of the actuarial reserve or an explicit profit surcharge was included in the contribution.

The evaluation method - i.e. the entire technical calculation basis - must be retained for the entire duration of the contract, unless there is a reason under commercial law to change it (continuity requirement). From a regulatory perspective, an even stricter rule applies to the “interest” calculation base.

Implicit and explicit method

When calculating the present value of the benefit, the future current expenses for the insurance company's operations, mainly administrative and collection expenses, are to be included (explicit method).

If the contributions, in accordance with Section 11 (1) VAG, have been agreed to be sufficiently high that they also cover the (cautiously) expected future current expenses according to the technical calculation bases for the actuarial reserve, the implicit method is also permissible under EU law. In this context, all current expenses, insofar as they are approximately proportional to the current contributions, are ignored in the actuarial value of the obligation. Equally, the applied contributions are reduced by at least the same amount ( zillmerized net contribution method ); the remaining amount is called the zillmerized net contribution. This means that the estimated value of the actuarial reserve can only increase; so the method is more careful. German law does not explicitly mention the implicit method, but allows the zillmert net contribution method and thus indirectly the implicit method. Basically, the applicability results from the equivalence to be proven with the explicit method, so that an express permission is not required. The implicit method is also predominantly used. However, it can only be used if the contribution period corresponds to the entire insurance period.

The implicit method can be used for contracts against a single premium or if the premium payment ends before the end of the insurance period (premium-free periods) if at the same time a partial provision for future expenses, the "administrative cost provision", is formed within the actuarial reserve ( Section 25 (3) RechVersV) . (Note: In actuarial mathematics, the term “ costs ” is used instead of the term “ expenses ” , whereby no clear distinction is made between the surcharges for costs in the contributions and the expected costs in the present value of the obligation.)

Consideration of acquisition costs

Acquisition expenses due at the start are not taken into account in a prospective procedure in the actuarial value of the obligation. Only acquisition expenses due later are to be taken into account as expenses for insurance operations up to the due date.

According to Section 11 (1) VAG, however, the insurers must take into account the expected acquisition costs when determining the premium. The actuarially determined present value of the contributions is accordingly higher than the actuarial value of the obligation immediately after the conclusion of the contract. When applying the realization principle, however, the situation directly at the time the contract is concluded, i.e. before any right or obligation on the basis of the contract has been fulfilled, is decisive. Therefore, in order to determine the requirement contribution, the initial closing expenses actually incurred must be added to the actuarial value of the obligation. This is because no unrealized profit is anticipated by applying these requirement contributions, which are increased by the initial closing expenses. The use of a lower requirement contribution would not give a true and fair picture of the asset, financial and earnings position, as the debts would be unnecessarily overvalued.

As a result, immediately after the conclusion of the contract, i.e. after the performance and thus the elimination of the recognized acquisition costs in the present value of the obligation, arithmetically negative actuarial reserves are to be recognized at zero.

The procedure and result with regard to the acquisition costs are also identical with the Zillmerten net contribution method, i.e. the implicit method described above. The use of the zillmerized net contribution method has no influence on the consideration of the closing expenses.

The consideration of acquisition costs is limited by supervisory law when determining the requirement contribution ( Section 4 Paragraph 1 and 4 DeckRV in conjunction with Section 65 Paragraph 1 No. 2 VAG in conjunction with Section 341e Paragraph 1 Sentence 2 HGB). Normally, a maximum of 2.5% (from January 1, 2015) of the sum of the contractual contributions may be set here. If the contract (as usual) provides for higher contributions that are not required for future obligations, these may not be taken into account in the present value of the requirement contributions in the actuarial reserve. They are therefore to be collected in proportion to the contributions at each contribution due. These excess premium components are traditionally referred to as "amortization surcharges", as they are primarily used in the insurer's internal accounts to offset acquisition costs of the insurer that are otherwise not covered in future periods. But they are effectively “profit surcharges”. "Profit surcharges" are the part of the contributions, which are not offset obligations under the same contract, so the profit sharing contribution, to win the insurer or to cover losses from other contracts.

Deterministic, stochastic and analytical method

With the deterministic method, the carefully determined expected value of the cash flows for this insurance year is estimated for each future insurance year. The sum of these amounts, discounted on the valuation date, is then the actuarial reserve. This is the actuarial reserve formula of traditional actuarial science.

With the stochastic method, a large number of scenarios of the development of the capital markets, the termination behavior, the mortality and the cost development are created. The course of the contract is simulated for each of these scenarios and the cash value of the resulting cash flows is determined. The sum of the present values ​​weighted with the (carefully chosen) probability of the respective scenario is then the actuarial reserve.

In the analytical method, the cash value of the cash flows is understood as a stochastic process . The analytically determined risk-weighted expected value of this process is then the actuarial reserve.

The stochastic method is only used in Germany in special cases to determine the actuarial reserve, but is predominant in some countries. In some modern types of contracts, e.g. B. the so-called " variable annuities " only the stochastic method can be used. The analytical method is mostly too complex to use. However, it is the most precise calculation method. In the case of a market-based valuation, but especially a valuation of financial guarantees, the stochastic method is preferred.

Consideration of the surrender value

Insofar as a contract provides for a contractually or legally determined surrender value that is above the actuarial reserve determined in accordance with commercial law requirements, the actuarial reserve must be increased to this amount ( Section 25 (2) RechVersV in implementation of a binding EU law requirement).

In conjunction with Section 66 of the VAG, this provision means that an insurer must hold so many investments at all times that it can satisfy all claims in the very unrealistic scenario of termination by all policyholders. Therefore, insurers are very reluctant to agree surrender values ​​that are higher than the otherwise applicable actuarial reserve. Although the relatively few people who terminate early have only a small advantage overall from these increased surrender values, the obligation to set up additional provisions for the entire portfolio and to make capital investments for this means significant financing costs that are disproportionate to the benefit of those who terminate early . These financing costs are charged to the services of all policyholders as they are of course allocated to the prices. Expressly for this reason, in its judgment on surrender values ​​in 2005 , the Federal Supreme Court only provided for a judicial amendment to the contract to the extent of a half division of the difference between a reimbursement and the originally intended surrender value, despite the lack of a contractual regulation on the surrender value . Insurers do not hesitate to pay increased surrender values ​​because they do not allow those who cancel the amounts, but because a legal situation punishing these increased surrender values ​​forces them to protect the interests of all policyholders.

Assumptions or parameters

Actuaries refer to the parameters with which the contributions and actuarial reserves are calculated using the deterministic method in traditional actuarial mathematics as the basis of calculation . With stochastic methods there are no calculation bases, only the probabilities of the selected scenarios (often several thousand) are used as assumptions. It is not possible to determine whether the choice of scenarios is one of the assumptions or the calculation method. In the analytical method, this applies to the choice of the stochastic process, which is also an assumption, but is the essential basis for the calculation method. The actual parameters here are the parameters required by the stochastic process for description. In this respect, the distinction between the technical calculation bases in "calculation method" and "assumptions" for stochastic or analytical methods does not make sense, since the method depends on the situation in the individual case.

In traditional actuarial mathematics, a distinction is made between the calculation bases in biometric calculation bases, for example mortality tables , the actuarial interest rate and cost rates.

Types of calculation bases

Biometric calculation bases are the parameters with which the insured risks, such as mortality , occupational disability or medical costs are modeled. As a rule, these parameters depend on gender and the age reached. In health insurance, cancellation probabilities are also used. Since December 21, 2012, the contribution agreement of newly concluded contracts can no longer differentiate according to the sex of the insured person . Therefore, no distinction is made according to gender when determining the actuarial reserve for these policies.

Since life and health insurance policies usually run for decades, future benefits and contributions are also discounted. The interest rate used here, which is traditionally the same for all periods of the payment flows, is known as the discount rate. The highest permissible actuarial interest rate for calculating the actuarial reserve for new business in life insurance is set out in Section 2 DeckRV. With exceptions (special tariffs, foreign currency insurance), it will be 1.25% from January 1, 2015. The maximum interest rate in health insurance is 3.5%.

The complete and careful mapping of future obligations from insurance contracts also includes the consideration of future expenses for insurance operations, in particular expenses for contract administration and premium collection, but also for the settlement of insurance claims. Therefore, the assumptions about future such expenses are also part of the calculation bases. Contribution parts that may not be received prematurely according to the realization principle or due to the maximum zillm rate are included in the calculation basis as "amortization surcharges" or "difference between standard and gross contribution" (profit surcharge).

Topping up the actuarial reserve in the event of an unfavorable change

According to Section 2 (2) DeckRV, the actuarial interest rate chosen at the time of conclusion of the actuarial reserve must be retained for the entire term of the contract, unless it has to be changed due to regulations. The other calculation bases may be changed in principle. But this is usually opposed by the principle of continuity and the principle of realization.

If, however, it turns out that the calculation bases originally estimated to be certain are not sufficient due to the later development, according to the imparity principle when calculating the actuarial reserve, the calculation bases used up to now are to be replaced by those which are currently sufficiently safe according to the current assessment. This leads to a corresponding increase in the actuarial reserve (“subsequent reservation”).

A recent example is the revaluation of pension insurance. It was found that the trends in mortality improvement included in the DAV 1994R table do not sufficiently take into account the actual increase in longevity. As a result, the life insurance companies had to assess the actuarial reserve for new business as of December 31, 2004 according to the DAV 2004R portfolio. The collateral included there will be expanded in the following years, provided that the trend assumed in the DAV 2004R table used for new business is confirmed in the respective year.

If it turns out that the current or expected investment income is not sufficient to meet the interest rate obligations entered into, the discount rate must be adjusted. The DeckRV specifies and lump-sum the corresponding commercial law requirements, but without releasing them from the obligation to comply with them. According to this, due to the low interest rate phase that has persisted in the capital markets for years, the discount rate to be used must be continuously reduced in accordance with a predetermined pattern. As of December 31, 2015, actuarial reserves may be calculated based on a discount rate of 2.88% ( maximum actuarial interest ). This means that the actuarial reserves are to be increased for the contract generations that were concluded before 2004 (apart from contracts from before mid-1986) without this increase being covered by contributions. The uncovered increase in the actuarial reserve is also referred to by actuaries as the “additional interest reserve”, as a difference to the originally “planned” actuarial reserve. In the following years, further significant reductions in the maximum actuarial interest rate and thus further increases in the actuarial reserves that are not covered by contributions, also for further contract generations, are to be expected. According to commercial law, the actuarial interest rate must in no way be lower than the expected return on investment of the insurer for the same period.

If the cost surcharges included are not sufficient to cover the actually expected future expenses, the mathematical reserve must be calculated with correspondingly higher cost rates.

In (private) health insurance, the basis of calculation of the contributions is always adjusted to current developments by means of premium adjustments and the bases of calculation used for the actuarial reserve follow these.


Responsible actuary

The responsible actuary certified under the balance a matching calculation with the rules of the mathematical provision by the insurer (actuarial confirmation in accordance with § 141 , para. 5 and § 12 , para. 3 VAG). In addition to the choice of an appropriate calculation method, the appropriateness of the choice of assumptions and parameters must also be confirmed.

In the new life insurance portfolio, the choice of the calculation bases is at the dutiful discretion of the insurer and within the legal requirements. Therefore, the responsible actuary has a special obligation to check the confirmation. In the old stock, the calculation is based on the approved business plan. In particular, compliance with the business plan must be checked and certified. The same applies to health insurance.

The responsible actuary has to explain in a report to the management board ("actuary report") which calculation approaches and assumptions are based on his confirmation. This does not apply to health insurances as well as death benefit funds and regulated pension funds. The actuarial report therefore explains why the actuarial reserve is based on appropriate technical calculation bases.


In practice, the actuarial reserve is usually determined for the beginning of the insurance year (anniversary of the insurance) before and after the balance sheet date and then interpolated to the reference date. A calculation with cash values ​​during the year is also possible. Insofar as annual premiums are actually charged by the policyholder for actuarial reserves calculated with annual contributions and interpolated in this way, the value of the actuarial reserve broken down into months must be supplemented by unearned premiums . The parts of the annual premium not taken into account in the actuarial reserve are accrued in these.

identification card

The cover provisions for commitments from unit- linked life insurance as well as tontines be in balance sheet format Form 1 of the RechVersV in the sub-item mathematical provision of passive post F. Technical provisions for life insurance where the investment risk is carried by the policy holders shown.

Incidentally, they are in the sub-item actuarial provision Liabilities item E. Technical provisions accounted for. For guaranteed minimum benefits from fund or index-linked contracts (or so-called hybrid products), an additional actuarial reserve must be created in this item, which represents the value of the guaranteed minimum benefit over and above the actuarial reserve already taken into account in liability item F.

In the case of property and casualty insurers, the actuarial reserves for liability and accident pensions are shown in the provision for claims that have not yet been settled (“ claims reserve”).

Share of reinsurers

The reinsurers' shares in the actuarial reserve are openly deducted from the gross amount in a column under the name Share for the insurance business given in reinsurance . The reinsurers deposit these and other amounts back with the primary insurer. This amount is shown under liability item H. Deposits from the insurance business given out in reinsurance .

The reinsurers hold shares in the actuarial reserve, provided that the reinsurance is based on the original. In the case of reinsurance on a risk basis or stop-loss contracts, the reinsurers have no share in the actuarial reserve.

international accounting

The valuation of the actuarial reserve according to German commercial and derived supervisory law is particularly careful, since a major task of commercial law is to protect creditors and of supervisory law to ensure that insurance contracts can be continuously fulfilled. The information function largely takes a back seat against this. International accounting and the US-GAAP often used by insurers are exclusively geared towards the information function. Therefore, there is often an earlier profit statement compared to the German accounting. Other calculation methods than the deterministic one are also increasingly used. It is to be expected that in the medium term international accounting will replace German accounting, also for insurers. The security of the insurer due to sufficient assets must then be guaranteed solely by regulatory law.

Special features in the individual insurance lines

In the case of personal insurers, the actuarial reserve is usually by far the largest liability item on the balance sheet.

Life insurance

The actuarial reserve in life insurance partly has the character of an aging reserve (provision of contribution parts for higher probability of death with increased age) and partly of a provision for future survival benefits (especially in the mixed insurance for death and survival and in pension insurance).

In addition to the actuarial reserve and the unearned premiums, another balance sheet item is calculated actuarially, namely the not yet due claims for repayment of paid, invoiced but not yet repaid acquisition costs. Insofar as the insurer is not only entitled to contract parts of the premium in general to cover all expenses from the insurance contracts, but also explicitly stipulates part of the premiums for covering the initial acquisition costs , according to the principles of proper accounting, in the case of partially fulfilled pending transactions, a claim to future, to cover contractually determined contribution parts to cover the acquisition costs already incurred. The assessment of this entitlement corresponds to the mathematically negative results in the calculation of the actuarial reserve, provided that this was not maximized to the surrender value. Otherwise, this increase amount will also be included in the claims, insofar as this is contractually or legally provided for. According to § 15 RechVersV, this balance sheet item is to be shown in the sub-item not yet due claims of claims from the direct insurance business against policyholders . The existence of such a claim depends on the agreements in the insurance contract. There is no connection with the calculation method for the actuarial reserve. It is often assumed that the approach to the claim depends on the zillmerization of the actuarial reserve. This is not the case, as the approach depends solely on the existence of the contractual agreement and must then also be carried out when using the gross premium method or methods other than zillmerization. The calculation method for the actuarial reserve itself is not part of the contractual agreements. Here, the insurer must observe the commercial law when choosing the calculation method.

Health insurance

In private health insurance , the actuarial reserve, referred to there as the aging reserve, essentially serves to compensate for the rising costs of illness with age: the policyholders pay constant contributions, but the expected benefits increase over time. In order to finance this effect, an aging reserve is built up in "younger" years, which is then "consumed" in old age.

In particular, the following must also be accounted for in the aging provision:

In health insurance, the negative and positive actuarial reserves of the individual policies are netted. If this results in an overall negative provision, it must be accounted for with zero. A cancellation provision must be set up in the other technical provisions for the cancellation of contracts with negative actuarial reserves .

Property and casualty insurance

Pension actuarial reserves for liability and accident pensions are shown in the claims reserve. Premium reserves, for example from accident insurance with premium refunds, are shown under the premium reserve item.

The same principles apply to the actuarial reserves of property and casualty insurers as in life insurance. In particular, the DeckRV is also to be applied here.

Individual evidence

  1. Art. 3 No. 2 Regulation of December 16, 2015 ( BGBl. I p. 2345 , PDF)
  2. Art. 1 No. 2 Regulation of December 16, 2015 ( BGBl. I p. 2345 , PDF)
  3. ^ BGH, judgment of October 12, 2005 , Az. IV ZR 162/03, full text.

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