Revisiting “networked networks”:: setting the scene for epic failure!


To say that there are those within the insurance industry who prefer the PR (or is it bs?) about insurance not being “systemically important” would be an understatement! But, I can almost forgive them their ignorance as they tend to be too busy doing what they have to do to survive, on a day-to-day basis, in difficult times. However, as someone who cares about the stability of the industry and a committed contrarian it would be wrong of me NOT to continue to advise and inform about something that could have such a significant upon their future financial well-being!

Quite apart from concerns about the behaviour of complex systems (see below), the insurance industry relies upon rating future risk based upon probabilities seen in incomplete data from past events, with an unhealthy smattering of assumptions for good measure…like Groundhog Day! But, even if this were as scientific as the industry would like us to believe, the risk models upon which they rely DO NOT/CANNOT cope with the non-linearity of a non-interacting network let alone that of interdependent networks (below).

Unfortunately, at the most senior levels, there is appears to be a belief that there is very little that can be learnt from observing other industries or, in fact, from nature itself. This has got to change and, I have no doubt, that it will but it is how that change comes about that really scares me because it could be painful and bloody as a result of the “close coupling” amongst insurers, reinsurers, banks, markets, institutional investors, etc.

These form global complex financial networks of systems and sub-systems at and across a variety of scales. They are robust yet fragile.

Inter-connectedness, flawed economic theory, years of pursuing self-similar [self-serving] strategies, that shaped belief systems [stifled creative destruction], behaviours and an, oft criticised, culture have seen them become excessively complex. Due to their close-coupling and burdened by complex regulation they lack the agility to adapt to survive in a rapidly changing and turbulent economic environment…

…but, then again, what do I know and who am I to disagree with powerful organisations that understand risk? Pity they aren’t prepared to learn more about complex systems and, as a precaution, focus upon systemic resilience!!!  

Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. Modern systems are coupled together15, 16, 17, 18, 19 and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures (‘concurrent malfunction’) is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations20. Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks.

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