Economics theories derived from academia are having an impact on the re/insurance business.

Re/insurance is not rocket science. But it's not kid's stuff either. Somewhere between the two is an increasingly sophisticated industry which is becoming ever more technical in its approach. It is still, however, some way behind other sectors of the financial community with regard to theory surrounding the way the market operates – one of the reasons why Global Reinsurance this year pioneered the Lumina Awards – but a change is upon us and new theories and techniques are beginning to grab hold. Although these have been the domain of actuaries, and many within the industry are happy to leave them there, these theories are more and more hitting the front line of the re/insurance sector.

Game theory is one of the areas that has been exercising minds. In the last few years, several academic studies proposed game-theoretical model to study various effects of scale in the primary insurance market. In particular, the works of Powers, Shubik and Yao (1994, 1998) and Powers and Shubik (1999) modelled their studies in such a way that that they could look at the marginal changes in competitive forces and in solvency when the number of market participants changed.

Balancing the options
Their works showed that there is a trade-off between the plus and minus sides of increasing the number of market participants. “As the number of firms increases, the weakening of the oligopolistic structure of the market improves efficiency, causing price to decrease and customers to purchase more insurance,” they explained. “However, the increasing number of firms also diminishes the ‘quality' of insurance (by lowering the average capital per firm, thereby increasing the probability of insurers default) eventually causing the customers to purchase less insurance. These two opposing influences determines an optimal number of firms – in terms of maximising the amount of insurance purchased – when the marginal changes are equalised.”

The next step for Michael Powers, chairman and associate professor in the department of risk, insurance and healthcare management at Temple University, and Martin Shubik, Seymour H. Knox professor of mathematical institutional economics at the Cowle Foundation, Yale University, was to factor in the reinsurance community. As a result, they developed a formal game theoretic model adding in the reinsurance community to the overall insurance industry.

In doing so, they came up against two major difficulties when studying the reinsurance community. The first was the international nature of the business. This made it hard to identify data belonging to transactions within one country – primary insurers frequently purchase reinsurance from organisations both within their own countries and overseas. Secondly, the boundary between primary insurance business and reinsurance often is hazy, with insurance companies frequently acting as reinsurers as well.

As a result, Powers and Shubik restricted their study to the US property/casualty insurers and US reinsurers that wrote no direct business. In 1996, this constituency comprised 3,300 primary insurance companies writing $250bn in premiums, and 72 reinsurers writing $19bn. Even so, they admit the sample may be skewed. “We note that this reinsurance market represents only about 20% of the global reinsurance market, and, most notably, excludes the London and Bermuda markets, which provide substantial capacity for US primary insurers.”

Consolidation activity
Between 1985 and 1996, the number of domestic US reinsurers fell from 97 to 72, a reflection of the consolidation activity in the market. Simultaneously, the market share of the ten largest reinsurers grew from 60% to 65% of the total market – an increase of 12.5%. The last decade saw the development of insurance-based securities, including property catastrophe indexes and catastrophe bonds. These have provide what Powers and Shubik described as “novel alternatives to traditional reinsurance products,” and they continued, “the increasing viability and popularity of these alternative products is undoubtedly one competitive force underlying the consolidation of the traditional reinsurance market.”

The equilibrium between the insurance and reinsurance markets has been studied over a number of decades, starting in the 1950s. It was in the 1980s, however, that game theory started being applied to the re/insurance market and its attitude to risk. Kihlstrom and Roth in 1982 analysed risk transfer between insurers within the parameters of co-operative game theory, and showed that the price of insurance would be actuarially fair under the model. But the later studies by Powers, Shubik and Yao applied a full market game structure to the primary insurance market. As Powers and Shubik noted, “For a one-period game in which the buyers and sellers of insurance make strategic bids and offers to determine market price and quantity, we were able to prove the existence and uniqueness of market equilibrium under certain conditions.”

Since that study, Powers and Shubik went on to apply the law of large numbers to the oligopolistic effect – market domination by a few participants – of the number of organisations in the market. When insurers had a risk-neutral attitude, there was a trade-off between the effects of the law of large numbers and oligopoly, they found.

Powers and Shubik have used game theory to develop a theory of reinsurance and retrocession in the light of the massive changes in the market over recent years, such as mergers and acquisitions, and new forms of risk transfer capital. Other studies have looked to apply game theory to other pockets of the industry. For example, Donald Mango of Crum & Forster four years ago looked at the application of game theory on property catastrophe risk load, concluding that not only were there more subtle methodologies for pricing, but also that advances in computer technology and modelling are now making “finer levels of analysis possible”.