Present Value Functions and Recursions

Abstract

g we define this random variable to be (,, ) PVA a x NDR when the person begins active and (, , ) PVA i x NDR when commencing inactive. We assume that future labor force activity status follows the usual Markov or increment-decrement model. In arranging these random variables into the row random vector     (, ) ( ,, ), ( , , ) P VA xN D R PVA axN D R PVA ix N D R , we provide a recursion for its probability mass function (often abbreviated “pmf” below), which we show to be computationally intractable. Next, we indicate how we may nevertheless estimate the probability mass function. We then provide a computationally useful recursion for its expected value  [( , ) ] EP VA x NDR . These expected values have been tabulated in the United Kingdom, where they are associated with the Ogden Tables. From another point of view,