Timed tuplix calculus and the Wesseling and van den Bergh equation

TL;DR

This paper introduces an algebraic framework based on timed tuplix calculus to formalize and analyze financial behaviors, including the conservation of interest, with properties of financial products derived within this formal system.

Contribution

It develops a novel algebraic formalization of financial behaviors incorporating timing and interest conservation, extending previous process algebra approaches.

Findings

Formalization of interest conservation in the framework

Definition of financial product behaviors within the algebra

Properties of financial behaviors derived from the formalization

Abstract

We develop an algebraic framework for the description and analysis of financial behaviours, that is, behaviours that consist of transferring certain amounts of money at planned times. To a large extent, analysis of financial products amounts to analysis of such behaviours. We formalize the cumulative interest compliant conservation requirement for financial products proposed by Wesseling and van den Bergh by an equation in the framework developed and define a notion of financial product behaviour using this formalization. We also present some properties of financial product behaviours. The development of the framework has been influenced by previous work on the process algebra ACP.