Examining the Problems with Traditional Risk Modeling Methods

Traditional financial risk management methods were formulated in an analogy with the early foundational principles of thermodynamics. However, traditional economic models are incomplete models of reality because economic systems are not inclined to attain equilibrium states unless we are talking about very short windows of time (similar to meteorological or most nuclear or gravitational systems).

Problems with risk modeling methods based on the laws of thermodynamics:

• Predictability is limited to short windows, where the initial conditions varies in small amplitudes and in small frequencies
• Complexities are dealt with once recognized, rather than as a result of structural evolution and systemic behavior of multiple-level interactions
• Only closed systems that reach equilibrium are dealt with, no adaptive ability to an external or internal modification is allowed
• Complex systems do not systematically expose equilibrium
• Using Stochastic models that deal with randomness are difficult to determine 
small resonances and therefore do not tend to a long term representation

A New Way to Look at Economy and Risk

Financial systems are not wholly physical. They do not always behave in an expected manner as predicted from their patterns of past behavior. They are immature. They can sometimes exhibit unexpected and unknown behavior because we do not understand their complexity and how it changes.

To avoid future crisis in the proportions of 2008, we must identify new methods of economic risk analysis that more accurately model the dynamic reality of financial systems. To this end, we promote determinism, which is the view that every event, including human cognition, behavior, decision, and action, is causally determined by an unbroken sequence of prior occurrences.

Determinists believe the universe is fully governed by causal laws resulting in only one possible state at any point in time. Simon-Pierre Laplace’s theory is generally referred to as “scientific determinism” and predicated on the supposition that all events have a cause and effect and the precise combination of events at a particular time engender a particular outcome.

How the impact of dynamic complexity leads to economy non-equilibrium:

• Different instruments within a portfolio have different dynamic patterns, evolution speeds, producing different impact on risk
• But also they influence each other: in sharing, affecting, and operating in terms of both frequency and amplitude in the behavior of discriminant factors (econometrics, relation economy/finance, long term repercussion etc.)
• In addition, each will have different reaction/interaction towards an external/ internal event.

Consequently, modeling economics dynamics is the right foundation to insure predictability of such self-organized evolutionary systems that may prevail towards even several points of singularities and larger number of degrees of freedom than the small number in traditional methods.

Using this method, we will be able to address most of the drawbacks of the traditional methods:

• Both the need for predictable determinism and the intensive presence of high level of dynamic complexity justifies the use of Perturbation Theory
• The condition of success to approach an exact solution at any moment of time relies on the use of deconstruction theory that will separate the constituents and find the proper mathematical expression of each prior to the deployment of the perturbed expression (i.e. two-level solution)
• Evolutionary process guarantees wider window of representativeness and adaptability for the dynamic complexityeconomics
• Tends to exact solution

Table: Dynamic Complexity versus Traditional Economics

Dynamic Complexity Economics	Traditional Economics
Open, dynamic, non-linear in equilibrium	Closed, static, linear in equilibrium
Each constituent of the system is model individually then aggregated through Perturbation Theory	The system is modeled collectively in one step
No separation between micro and macro level behaviors	Separation between micro and macro level behaviors
Evolutionary process guarantees wider window of representativeness and adaptability for the dynamic complexity economics	Unstable for wider windows of time
Allows for continuous interactions of external and internal agents	Does not allow for continuous interactions of external and internal agents
Optimal control is possible as sub product of dynamic complexity modeling	Optimal control is not possible

Conclusion

From a scientific standpoint, the subject of financial dynamics and the best risk analysis method is still open and further mathematical, physical and engineering as well as economic risk analysis developments are necessary. A great body of contributions, covering a wide spectrum of preferences and expertise and from deeply theoretical to profoundly pragmatic, currently exists today. All show the interest, but also the urgency, to find a solution that can help us avoid the singularities that occurred in 2008. To progress, we must continuously seek to recognize the failures of past methods and strive to find solutions.