Titlebook: Life Insurance Mathematics; Hans U. Gerber Textbook 1997Latest edition Springer-Verlag Berlin Heidelberg 1997 Excel.Finance.Lebensversiche

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y and the emerging dynamic models based on stochastic processes and the modern theory of finance. The structure of the bridge is very solid, though at the same time pleasant to walk along. I have no doubt that Gerber‘s book will become the standard text for many years to come. .Metrika, 44, 1996, 2.978-3-642-08285-6978-3-662-03460-6

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Expense Loadings,nsurance companies, on the other hand, the cost element is built into the model, as explicitly and equitably as possible. As we shall see, however, the resulting premiums and reserves are very closely related to the net premiums and reserves we have been discussing so far, and which will therefore continue to hold our primary interest.

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978-3-642-08285-6Springer-Verlag Berlin Heidelberg 1997

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Life Insurance,Under a life insurance contract the benefit insured consists of a single payment, the . The time and amount of this payment may be functions of the random variable . that has been introduced in Chapter 2. Thus the time and amount of the payment may be random variables themselves.

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Life Annuities,A life annuity consists of a series of payments which are made while the beneficiary (of initial age . lives. Thus a life annuity may be represented as an annuity-certain with a term dependent on the remaining lifetime .. Its present value thus becomes a random variable, which we shall denote by Y.

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Net Premiums,An insurance policy specifies on the one hand the benefits payable by the insurer (benefits may consist of one payment or a series of payments, see Chapters 3 and 4), and on the other hand the premium(s) payable by the insured. Three forms of premium payment can be distinguished:

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Net Premium Reserves,Consider an insurance policy which is financed by net premiums. At the time of policy issue, the expected present value of future premiums equals the expected present value of future benefit payments, making the expected loss . of the insurer zero.

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