SOME MATHEMATICAL PROPERTIES OF THE PRICE OF AN ARBITRAGE PROFITABLE RISKLESS BOND

Abstract

It is well known that a discounting function describes the price of a default free bond. In this paper, some mathematical properties of this function are studied when it is subadditive. Subadditive discounting means that the total discount is minor when the year is divided into months and implies that the more divided the interval is into subintervals, the smaller the total discount will be. First, two sufficient conditions for a discounting function being subadditive (resp. superadditive) are shown; more precisely, the increase (resp. decrease) of the instantaneous discount rate and certain integral inequality are proposed as such sufficient conditions. On the other hand, the convexity (resp. concavity) of the Napierian logarithm of the discounting function is shown as a particular case of another more general sufficient condition. Finally, under certain conditions, subadditive discounting functions are necessarily regular.