Differential rates, residual information sets and transactional algebras

The purpose of this paper is to model differential rates over residual information sets, so as to shape transactional algebras into operational grounds. Firstly, simple differential rates over residual information sets are introduced by taking advantage of finite algebras of sets. Secondly, after contextual sets and the relevant algebra of information sets is suitably fashioned, generalized differential rates over residual information sets are expanded on, while a recursive algorithm is set forth to characterize such rates and sets. Thirdly, the notion of transactional algebra is presented and heed is given to the costs of running such structure. Finally, an application to financial arbitrage processes is fully developed within a transactional algebra, setting up arbitrage returns net of transaction costs, establishing boundary conditions for an arbitrage to take place, and finally allowing for a definition of what should be meant by financial arbitrage within a transactional algebra.