Quantitative Description of Financial Transactions and Risks

This paper presents a quantitative model of financial transactions between economic agents on economic space. Risk ratings of economic agents play role of their coordinates. Aggregate amounts of agent's financial variables at point x define macro financial variables as functions of time and coordinates. Financial transactions between agents define evolution of agent's financial variables. Aggregate amounts of financial transactions between agents at points x and y define macro financial transactions as functions of x and y. Macro transactions determine evolution of macro financial variables. To describe dynamics and interactions of macro transactions we derive hydrodynamic-like equations. Description of macro transactions permits model evolution of macro financial variables and hence develop dynamics and forecasts of macro finance. As example for simple model interactions between macro transactions we derive hydrodynamic-like equations and obtain wave equations for their perturbations. Waves of macro transactions induce waves of macro financial variables on economic space. Diversities of financial waves of macro transactions and macro financial variables on economic space in simple models uncover internal complexity of macro financial processes. Any developments of financial models and forecast should take into account financial wave processes and their influences