  In a series of precedent papers, we have presented a comprehensive
methodology, termed Field Economics, for translating a standard economic model
into a statistical field-formalism framework. This formalism requires a large
number of heterogeneous agents, possibly of different types. It reveals the
emergence of collective states among these agents or type of agents while
preserving the interactions and microeconomic features of the system at the
individual level. In two prior papers, we applied this formalism to analyze the
dynamics of capital allocation and accumulation in a simple microeconomic
framework of investors and firms.Building upon our prior work, the present
paper refines the initial model by expanding its scope. Instead of considering
financial firms investing solely in real sectors, we now suppose that financial
agents may also invest in other financial firms. We also introduce banks in the
system that act as investors with a credit multiplier. Two types of interaction
are now considered within the financial sector: financial agents can lend
capital to, or choose to buy shares of, other financial firms. Capital now
flows between financial agents and is only partly invested in real sectors,
depending on their relative returns. We translate this framework into our
formalism and study the diffusion of capital and possible defaults in the
system, both at the macro and micro level.At the macro level, we find that
several collective states may emerge, each characterized by a distinct level of
average capital and investors per sector. These collective states depend on
external parameters such as level of connections between investors or firms'
productivity.The multiplicity of possible collective states is the consequence
of the nature of the system composed of interconnected heterogeneous agents.
Several equivalent patterns of returns and portfolio allocation may emerge. The
multiple collective states induce the unstable nature of financial markets, and
some of them include defaults may emerge. At the micro level, we study the
propagation of returns and defaults within a given collective state. Our
findings highlight the significant role of banks, which can either stabilize
the system through lending activities or propagate instability through loans to
investors.
