Abstract
The analysis of stochastic present value models provides one of the more powerful techniques applicable to financial decision making under conditions of uncertainty. The paper introduces a present value model for a random payment decomposed into a random sum of continuous positive independent and identically distributed random variables, under a random timing represented as the minimum of a random number of continuous positive and identically distributed random variables. Properties of the corresponding distribution function are established. Moreover, the paper provides applications of the model in selecting risk management processes for a system consisting of a random number of components, each component having a random failure time.
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