Structures on the space of financial events

Abstract

In this paper we endow the space of financial events with some structures, each of them represents basic facts of financial mathematics. We introduce a preordered structure, that we shall call the usual preorder of the financial events plane, and an algebraic structure, that we call the usual linearoid structure of the financial events plane. The algebraic structures introduced are not void of properties: the usual addition will confer to the space a gruppoid structure and the multiplication by scalars will be a law of action associative and distributive with respect to the addition. We shall prove that these structures are compatible among them and with the standard topology of the plane. Then we show the possibility of defining new (economically relevant) preorders by the use of capitalization factors and that there is a manner (the conjunction) to obtain the usual preorder from infinite continuous families of these new preorders induced by a capitalization factor.