### Incorporating Random Contractions in Decision Support Systems for Facilitating Synergies of Proactivity and Extremity

#### Abstract

The paper formulates a stochastic model by introducing the present value of a continuous uniform cash flow, with rate of payment and duration being random and force of interest being constant, in the maximum of a random number of positive random variables. The paper also provides an interpretation and practical applications of the stochastic model. Moreover, the paper establishes sufficient conditions for the representation of the stochastic model as the maximum of a random number of random contractions. In addition, the paper makes clear that the structural elements, the principal components, and the mathematical form of the stochastic model facilitate the development of synergies between the concepts of extremity, proactivity, and information for supporting intelligent systems.

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DOI: http://dx.doi.org/10.26713%2Fjims.v12i1.1224

eISSN 0975-5748; pISSN 0974-875X