Random Variables, the Time Value of Money and Capital Expenditures - Kabak, Irwin W.; Owen, Joel (Management Science, 1970)
This paper treats the following problem. How much money should be invested at time t 0 at an interest rate of I for a time T such that the probability of the funds required “K(T)” exceeding those available “X(T)” equals at most p. That is PK(T) > X(T) ≤ p, where X(T) = X(t 0 ) exp I(T − t 0 ). The parameters I, T, X(T) and K(T) are taken to be random variables. The theory to solve the stated problem is presented and solutions to certain specific cases are given.