Narrow Results

The aim of this paper is to create a platform for developing an interface between the mathematical theory of reliability and the mathematics of finance. This we are able to do because there exists an isomorphic relationship between the survival function of reliability, and the asset pricing formula of fixed income investments. This connection suggests that the exponentiation formula of reliability theory and survival analysis be reinterpreted from a more encompassing perspective, namely, as the law of a diminishing resource. The isomorphism also helps us to characterize the asset pricing formula in non-parametric classes of functions, and to obtain its crossing properties. The latter provides bounds and inequalities on investment horizons. More generally, the isomorphism enables us to expand the scope of mathematical finance and of mathematical reliability by importing ideas and techniques from one discipline to the other. As an example of this interchange we consider interest rate functions that are determined up to an unknown constant so that the set-up results in a Bayesian formulation. We may also model interest rates as “shot-noise processes”, often used in reliability, and conversely, the failure rate function as a Lévy process, popular in mathematical finance. A consideration of the shot noise process for modelling interest rates appears to be new.