Do disease models provide any insight into the control or mitigation of more serious insurance contagion? ask Dewi James and Richard King

Diseases like AIDS, SARS and malaria are smart, they exploit their host's biochemistry, the social structures of the host population (the "herd" behaviour) and intermediate hosts for transportation. The high social and economic cost of such diseases has naturally led to the development of strategies to mitigate their impact, principally promoting lifestyle change, immunisation programmes, removal of the habitats of the intermediate disease carriers and, in extreme cases, isolation of the infectious groups.

The financial and other networks that exist amongst insurers, reinsurers, brokers, capital providers, regulators and other parties in our markets bear striking similarities to the populations that have been the subject of much research in the field of epidemiology. Epidemiologists are interested in the spread of disease through networks of susceptible individuals; insurance analysts with the spread of claims. So, do epidemiological models provide any useful insights for insurers dealing with the more serious claims scenarios?

THE EPIDEMIOLOGICAL MODEL

Disease models subdivide populations into distinct classes according to their experience with respect to a disease. One of the simplest models is the "SIR" model, which consists of three classes: Susceptible, Infectious and Recovered. Individuals move between classes according to very simple rules - individuals are born Susceptible, the Infectious pass diseases to the Susceptible and those that recover acquire some immunity and are less likely to be re-infected. The ability of a disease to spread depends on the opportunity it gets to contact Susceptible individuals, the virulence of the pathogen, and the degree of immunity, or improved behavioural and risk avoidance strategies induced amongst the Recovered class. Epidemiological models can of course be far more sophisticated, incorporating many member classes with complex interactions to model the transition of individuals between classes and hundreds of parameters describing the biology of a pathogen, social interactions of the hosts and transport vectors amongst host populations.

THE BASIC REPRODUCTIVE RATIO

A fundamental measure in epidemiological models is the number of secondary cases of a disease which a single carrier will give rise to in a population having no immunity, this is known as the "basic reproductive ratio" - R0.

Insurance and reinsurance has its own "insurance" R0. The analogy to this concept is most acutely observed in the retrocession market and in particular the personal accident (PA spiral) and the London market excess of loss market (LMX spiral) of the late 1980s. Mutual retrocession relationships (largely unplanned) cause recycling of the same losses leading to accounted gross losses of many multiples of the original claim to the market, with all the attendant frictional costs, exposure to counterparty credit risk and reserving problems. For the major LMX catastrophes of this era multiples of up to ten were possible and, for the PA spiral, even higher multiples occurred.

Public health bodies use the basic reproductive ratio, coupled with knowledge of the transmission mechanisms, to select the most effective control measures for particular diseases. Vaccination is the most common technique and this works by infecting a large class of the population with a weak, non-damaging dose of the disease in order to induce the production of antibodies, which will be an effective defence against the full-strength pathogen.

In other words, vaccination programmes infect the Susceptible class of individuals in order to artificially create a larger class of, in effect, Recovered individuals - a firebreak.

A feature of the simple SIR model is that it produces a stable mix of the distinct population classes and, conveniently, the ratio 1/R0 gives the proportion of Susceptibles in a population. The significance of this is demonstrated by reference to table 1.

A key question for public health management is the required scale of a vaccination programme in order to guarantee its success. The theoretical threshold for the proportion of the population to be vaccinated is given by VT = 1 - 1/R0. Based on this formula it can be seen that for malaria more than 99% of the Susceptible population would require vaccination.

This level of vaccination is not possible, so a more effective strategy is to attack the intermediate host - the mosquito. However, for smallpox VT is around 70% and, with careful targeting, vaccination has been highly successful and has eradicated this disease. AIDS is somewhat different and there is no vaccination as such, so public health strategies have focussed on behavioural change and treatment of the symptoms. Clearly, each disease affects individuals and societies in different ways and the lessons learnt in dealing with one problem are carried into treatments for other diseases.

THE INSURANCE ANALOGY

The experience of the late 1980s in the LMX market drove home the message that knowledge of the counterparties, whether as cedants or as reinsurers, was vital in order to control the extent of aggregate exposures to catastrophe events. In the absence of such detailed information, other strategies are needed to reduce the insurance R0 phenomenon.

Mitigation strategies that have evolved in reinsurance include:

Co-insurance clause - the cedant is forced to retain some of the pathogen, reducing the ability of claims to propagate further up the food chain - a form of vaccination.

Exclusion clause - isolates the exposure base from a particular form of claim.

Claims cooperation clause - reinsurers are exposed to a moral hazard when the cedant is certain to exhaust its retention. This potential change in behaviour by the cedant presents claims with an opportunity to broaden the spread of infection. It is often therefore in the interest of the whole community to collaborate in mitigating the claims outbreak at source in order to reduce the overall scale of the epidemic. This form of claims and risk management is a combination of modifying the herd behaviour and the removal of the source of risk.

Commutation - this activity is significant in limiting the ability of claims to pass between cedant, reinsurer and retrocessionaire. It is essentially a form of vaccination, whereby the reinsurer settles for a discounted value which is then often compromised in its ability to collect the appropriate commuted amount from its own reinsurers.


The mitigation strategies described are principally forms of vaccination, causing the retrocessional system to "leak" a greater proportion of claims as they attempt to recycle themselves. This is consistent with public health vaccination programmes given that most of the time catastrophes probably experience an insurance R0 lower than 10.

THE FUTURE

Insurers' and reinsurers' self-medication seems to revolve around vaccination of various forms, and whilst regulators and rating agencies provide a limited health check, they focus mainly on individual institutional risk, not systemic risk. Meanwhile, networks of financial institutions are connected in ever more complex ways, providing more opportunity for catastrophic claims to weaken financial systems - paths are being created for claims where vaccination is not the best strategy. This suggests that a clearer understanding of the relationships between market participants must be developed.

The choices are: try to understand how networks interact, develop comprehensive models of alternative scenarios and identify the key dependencies and formulate pre-emptive measures; or take our chances in the knowledge that each individual knows best.

History undermines the latter as a responsible model. The former introduces an almost Orwellian demand for perfect information. How might this be achieved?

Regulators and the rating agencies simply cannot know the "connectedness" of the whole insurance population.

Reinsurance is starting to be placed electronically through trading hubs; if this continues then it will enable the creation of comprehensive dependency models. The press of a button could generate virtual loss events and track their path through the entire reinsurance community.

Obligatory cessions to a state reinsurer would quite rapidly generate a central database of all reinsurance transactions - perfect knowledge, but only in respect of contracts which they are obliged to receive.

In an industry still in love with the market, should we prefer reinsurance brokers to act as steward? They capture data to administer transactions but a little collaboration would permit a database of relationships to be used to test market resilience to various loss events.

Commercial entities tend to be secretive, perhaps understandably. The co-operation required to understand the dependency problem is unlikely to be achieved, but that doesn't mean that awareness of potential pitfalls should not be raised. Call it an underwriting health check - who you get into bed with can be a life-changing decision. Who (and how) you reinsure can have similar implications.

- Dewi James (djames@james-brennan.com) is chief actuary at James, Brennan & Associates and Richard King is a senior consultant with Helix UK.