Technical Provisions - Life Insurance Reserves

Wednesday, 11 May 2011 18:58

Technical Provisions - Life Insurance Reserves

Technical provisions - life insurance reserves : are established by insurers (mostly as the book costs according to law) to fulfil obligations arising from insurance activities (such obligations are probable or certain, though their amount or time may be still uncertain).

The life insurance reserve - technical provisions are important statutory liabilities of each insurance company that are conform to special accounting principles and tax regulations; the assets covering the technical provisions are subject to strict investment restrictions since their financial placement should fulfil principles of prudence, diversification, profitability and liquidity; according to particular insurance legislations, various technical provisions may be established in life insurance (see also Sect. 21.4 for non-life insurance):

- premium reserve: must be established due to the fact that at time t (t >0) following the policy issue (t = 0) there is no longer an equivalence between future financial obligations of the insurer and the policyholder: the expected present value of future benefits will always exceed the expected present value of future level premiums at time t; this fact implies a positive difference which is a significant life insurer's liability called the premium reserve; moreover, one distinguishes (1) gross premium reserve (also called expense-loaded premium reserve), if the expenses by life insurer (see Sect. 18.2) are included, and (2) net premium reserve, if it is not the case; the difference between the sum insured and the premium reserve (net or gross) is called the amount at risk

- life insurance reserve for unearned premium ( technical provisions ): corresponds to such a part of the written premium that relates to future accounting periods; e.g. a quarter of an annual premium paid at the beginning of October covers the rest of the current year of account (the so-called earned premium), while the remaining three quarters (the so-called unearned premium) relate to the first 9 months of the next year of account so that one must establish the reserve for unearned premium in the current year of account for this purpose

- claim reserve: covers obligations due to insured events (claims) which in the current accounting period have been:

reported but not settled (the so-called RBNS reserve)
incurred but not reported (the so-called IBNR reserve)

(the claim reserves use not to be significant in life insurance (unlike the nonlife insurance, see Sect. 21.4))

reserve for bonuses and rebates: covers costs of bonuses and rebates guaranteed by insurance policies
life insurance reserve where investment risk is borne by policyholder: applies to unit-linked insurance products (see Sect. 19.3)
other life insurance reserves approved by authorities (by the state insurance supervision)

Denotation for life insurance reserves:

tZ random variable representing the present

value of insurance benefits (see Sect. 6.1) calculated at time t (t >0) following the policy issue (t = 0) by means of the technical interest rate (see Sect. 18.1) tPV = E(tZ) expected present value of insurance benefits

calculated at time t (see thereinbefore) tPVP expected present value of insurance premi

ums calculated at time t tVx = tPV - tPVP net premium reserve at time t for a life aged

x at entry (prospective method: the reserve is calculated as the net expected loss by insurer at time t (0Vx = 0))

tFV expected future (i.e. final) value of insurance

benefits (see Sect. 6.1) calculated at time t tFVP expected future (i.e. final) value of premiums

calculated at time t

tVx = tFVP — tFV net premium reserve at time t for a life aged x

at entry (retrospective method: the reserve is calculated as the net past profit by insurer at time t (0Vx = 0); the method gives the same result as the prospective one (see thereinbefore))

tPVE expected present value of expenses by insurer

calculated at time t

tVxgross = (tPV + tPVE) — tPVP gross premium reserve (also called expense-

loaded premium reserve) at time t for a life aged x at entry (prospective method: the retrospective one is analogous)

• Formulas of the net and gross premium reserves for particular insurance products (see thereinafter) are presented in the prospective form (in practice, the prospective formulas are preferred since (1) they enable to carry out comfortably various future changes in the insurance policy; (2) they may be simpler at time t than the retrospective ones when premiums are no longer collected at time t (in particular, this scenario holds for products with single premiums)):

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(net premium life insurance reserve at the end of the year t of an n-year insurance for a life aged x at entry (analogously for perpetual insurances): Px:n-\ is the annual premium paid always at the beginning of further year of insurance; at is the stipulated benefit paid on survival of the end of the year t of insurance; bt is the stipulated benefit paid at the end of the year t of insurance on death within this year; when premiums are no longer collected at time t (in particular, in products with single premiums), then the second term (the subtrahend) in the given formula is dropped out; some insurance products (e.g. the term insurance, see Sect. 18.5) establish so small premium reserves that such reserves may be ignored in practice: hence the insurance products may be classified to capitalizing and non-capitalizing ones)

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(retrospective form of net premium reserve: is equal to the prospective one (see thereinbefore); the retrospective form is not usual in practice)

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(recursive form of net premium life insurance reserve ( technical provisions) : is used to derive some relations, e.g. to decompose the period premium to the saving premium and the risk premium (see thereinafter))

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(saving premium at time t: serves to increase the net premium reserve at the beginning of the year t in addition to the interest compounding; risk premium at time t: covers on average the risk that the insurer will pay off at the end of tth year the benefit amounting at ¦ px +1—1 ¦ v + bt ¦ qx +1—1 ¦ v = at ¦ (Dx + D +1—1) + bt ¦ (Cx + t—1/Dx +1—1) making use of the fund tVx:n\ ¦ qx +1— 1 ¦ v = tVt:nl ¦ (Cx + t—1/Dx +1—1) released from the net premium reserve due to death event within the year t (see e.g. Sect. 18.6 for the endowment); if the death event occurs in a capitalizing product (see thereinbefore), then the sum insured required from the insurer as the benefit is composed by two sources: (1) by the net premium reserve established by saving premiums of the given policyholder and (2) by the amount at risk (which is the difference between the sum insured and the premium reserve at the given time) established by risk premiums of all policyholders (the mechanism works in such a way that the amounts at risk for the policies with death events are covered by risk premiums across the whole insurance portfolio))

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(gross premium life insurance reserve for periodic premiums (analogously for perpetual insurances): in contrast to the net premium reserve, the new business commission aN (i.e. the first-year provision, see Sect. 18.2) symbols in the formula; the term which is subtracted from the net premium reserve in the formula is called the zillmerising term (or the negative acquisition expenses reserve); its subtraction from the net premium reserve is called zillmerisation and has the following interpretation: (1) the new business commission aN (amounting significant values nowadays) is expended by the insurer immediately at the time of policy issue ^ (2) however, this amount due is paid back gradually in particular periodic premium payments (hence, the insurer becomes the "creditor" of the policyholder) ^ (3) therefore at the given time t the insurer always reduces the net premium reserve by the non-amortized part of the new business commission at time t, which is just the zillmerising term at time t; the zillmerisation may produce negative values of the gross premium reserve (usually in initial years of long-term policies), which are mostly replaced by zero values in practice)

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(gross premium life insurance reserve for single premium (analogously for perpetual insurances): in contrast to the net premium reserve, the expenses aC and y (see Sect. 18.2) symbol in the formula; the term which is added to the net premium reserve in the formula should just cover these future costs)

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(net premium reserve at fractional durations: monthly values of the net premium reserve with monthly premiums (analogously for perpetual insurances or for gross premium reserves at fractional durations))

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(net premium reserve at fractional durations: monthly values of the net premium reserve with annual premiums (analogously for perpetual insurances or for gross premium reserves at fractional durations)).