Actuarial values of payment streams

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Abstract
The coverage of life insurance (i.e., contingencies like death, survival, disability, widowhood, orphanhood) can be modelled by stochastic processes in discrete or continuous time. This paper focuses on the time-continuous case and describes general annuities by means of indicator processes while general assurances are described as counting processes. Cash values of corresponding payment streams are represented as stochastic integrals, whose expectancies are usually called actuarial values. General formulas of the latter are proved, along with formulas for corresponding cross-product moments.