We must start with what the theory of emergence means. Emergence spawned from cosmology, the study of the cosmos. Within cosmology the origins and evolution of the universe are explained. If we start at the big bang, this event led to further particle evolution and emergence of materials was set forth. For example, within unified string theory there are membranes behind the singularity of the big bang that intersected releasing all the energy in our present universe. As this released energy turned into plasma and cooled, other forces and particles emerged from the singularity. This emergence of subatomic particles led to hydrogen and star formation. Within these first stars further nucleosynthesis continued and produced heavier atoms. This process continues leading to further complex arrangements of life, e.g. social organization.
Economic or financial emergence is similar to cosmological emergence. Within economic emergence there are the following: (a) economic development, (b) systemic risk, and (c) contagion. Economic development can be easily explained in the stages of growth of a society. For example, a hunting and gathering society evolving into a domesticated farming community shows the emergence of higher social order.
In terms of systemic risk, financial systems are complex systems and these systems can behave in unexpected ways. Systemic risk usually evolves from a somewhat benign state to a much more malignant state, whereby it reaches escape velocity and threatens the financial fabric of a society (Cottrell, 2014). During the malignant state of systemic risk, contagion spreads. For example, during the subprime crisis in 2007 many bond holders were suffering losses. At a myopic perspective, subprime borrowers should not have affected the overall economy in theory, but it did—leading to the commercial paper markets freezing up. The key takeaway is that a complex system can evolve into unpredicted pathways; hence this follows the concept of non-deterministic chaos.
Complexity science is the study of complex systems. Within complex systems there are agents that are defined with basic rules of interaction. Within the state space that agents operate self–organizing behavior emerges over time. Within these self–organizing behaviors we have interactions that have magnifying effects.