Continuous Time Macro-Finance, Financial Transactions and Waves

This paper describes continuous time macro-finance via dynamics of financial transactions between economic agents. Risk ratings of agents play role of their coordinates x on economic space. Financial variables of agents like Investment or Assets, Profits or Credits allow describe corresponding macro financial variables. Aggregates of financial variables of all agents allocated near x define macro variables as functions of time and x. Integrals of financial variables over economic space equal common variables of entire macro-finance as functions of time only. Financial transactions between agents define evolution of their financial variables. Aggregates of financial transactions between agents allocated at points x and y define macro transactions that describe financial "action-at-a-distance" between points x and y. Dynamics of macro transactions define evolution of macro financial variables. To model macro financial transactions and their mutual interactions we obtain hydrodynamic-like equations. For simple model of interactions between two macro transactions like Assets-Liabilities and Income-on-Assets we derive hydrodynamic-like equations in a closed form. That allows model relations between two macro transactions in a self-consistent manner. For that model we derive wave equations on perturbations of macro transactions and study simple solutions and consequences. Existence and diversities of financial waves in simple models clarifies importance of wave processes for macro-finance modeling