Payment Measures, Interest, and Discounting

Abstract

Streams of payments are represented as measures on the real line. A wide class of consistent rules for evaluation of payment streams are determined from a set of basic axioms. Additional regularity requirements lead to valuating any payment stream by the integral of a positive discount function with respect to the payment measure. Inter-relationships between generalized annuities and lump sum payments are obtained by the general rule of integration by parts. By placing probability distributions on the payment measures and possibly on the discount function, a wide class of actuarial and related problems are put on the same footing.

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