Formulations and Investigations of Random Contractions

Abstract

AbstractThe contribution of the third chapter consists of the implementation of several theoretical and practical purposes related to the formulation of a stochastic multiplicative model, the representation of the formulated stochastic multiplicative model as a random contraction, the explicit analytical evaluation of the characteristic function corresponding to such a random contraction, the interpretation of the formulated stochastic multiplicative model and the related random contraction as a stochastic discounting model, and the explicit analytical evaluation of the characteristic function corresponding to such a stochastic discounting model. The chapter also establishes an extension of the formulated stochastic multiplicative model by incorporating a positive random variable and a Bernoulli random variable and the representation of the formulated stochastic model as a random contraction. The explicit analytical evaluation of the characteristic function and the establishment of a characterization of such an extension constitute new results of the third chapter. The chapter also includes the representation of the extension of the formulated stochastic multiplicative model and the related random contraction as a stochastic discounting model. The explicit analytical evaluation of the characteristic function is also provided.KeywordsRandom contractionStochastic multiplicative modelStochastic discountingCharacteristic function