CONTENTSIntroduction......................................................................................................................................... 51. n-Monotonic functions on (— ∞, ∞)........................................................................................... 62. Order relations in the set of probability distribution functions....................................................... 12 2.1. Preliminary concepts...............................................................................................................

This note reviews how the contemporary concept of the Poisson process (sometimes called the Poisson random measure or Poisson point process) evolved through out the time up to recent times. That is from F. Lundberg and W. Feller up to A. Renyi (1967) paper and finally, a construction of Poisson processes by binomial (or Bernoulli) processes, which can be found in J.E. Moyal (1962), J. Mecke (1967) and J.F. Kingman (1967) papers. Also in C. Ryll-Nardzewski (1953) this construction was used in the...

The authors review and criticize different approaches for calculations of ruin probabilities in one or multiperiod life insurance portfolios. They claim that precise calculations are time-consuming and in some cases (especially in the multiperiod ones) are practically inaccessible even if theoretical formulae are available. The reviewer considers that, because parameters of any such model must be estimated somehow, then precision in calculations cannot be achieved. For example, the authors assume...

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