Incorporating a random number of independent competing risks in discounting a continuous uniform cash flow with rate of payment being a random sum

The concept of minimum of a random number of positive, independent and identically distributed random variables and the concept of sum of a random number of positive, independent and identically distributed random variables are particularly important in many theoretical and practical disciplines. The paper introduces these concepts into the stochastic model denoting the present value of a continuous uniform cash flow with constant force of interest. The paper also establishes sufficient conditions for embedding the stochastic model into the class of stochastic multiplicative models based on two positive and independent random variables. Moreover, the paper provides applications of the stochastic model in the area of independent competing risks.