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Titlebook: Life Insurance Theory; Actuarial Perspectiv F. Etienne Vylder Book 1997 Springer Science+Business Media Dordrecht 1997 development.differen

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Life Insurance Contracts (One Life),A . on the life x is a couple (C. P.) of time-capitals C. and P. depending on x. The time-capital C. is the . to be paid to x and P. is the . x to be paid to the insurance company (see Ch.4.2). For the moment no expense-loadings are taken into account, i.e. only .. In practice, C. and P. are ., i.e. time-capitals with positive amounts.
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Ruin Probability of a Life Insurance Company,Let us call . and ..., those used by the insurer in the evaluation of present values, prices, premiums and reserves. The technical interest rate i is different from the . i* produced by reserves and the technical mortality is not necessarily the same as the ..
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Decompositions of Time-Capitals (Several Lives),For simplicity, only time-capitals on two lives x and y are treated in this Chapter. All definitions and proofs are easily adapted to the case of more lives.
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Variances (Several Lives),The considerations of Ch.10.1–11 can obviously be adapted to life portfolios with policies on any number of lives.
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Basic Concepts of Live Insurance Mathematics,ate i) and the classical mortality model (with survival probabilities resulting from a continuous life table ..). The classical life insurance model is adopted if nothing else is stated explicitly. Some developments have direct generalizations in case of variable interest rates: it is enough to replace the discount factor v. by v., everywhere.
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Multiple Decrement Models, τ. An arrow from state α to state β indicates that a . from state α to state β can occur at some moment. Such an arrow can exist if α<β only (the latter condition is dropped in case of .. see last part of section 14.3).
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