Insurance loss coverage under restricted risk classification

Insurers hope to make profit through pooling policies from a large number of individuals. Unless the risk in question is similar for all potential customers, an insurer is exposed to the possibility of adverse selection by attracting only high-risk individuals. To counter this, insurers have traditionally employed underwriting principles, identifying suitable risk factors to subdivide their potential customers into homogeneous risk groups, based on which risk-related premiums can be charged.

In reality, however, insurers may not have all the information reflecting individuals' risks due to information asymmetry or restrictions on using certain risk factors by regulators. In either case, conventional wisdom suggests that the absence of risk classification in an insurance market is likely to lead to a vicious circle: increasing premium with the prime aim to recover losses from over-subscription by high risks would lead to more low risks dropping out of the market; and eventually leading to a collapse of the whole insurance system, i.e. an adverse selection spiral. However, this concept is difficult to reconcile with the successful operation of many insurance markets, even in the presence of some restrictions on risk classification by regulators.

Theoretical analysis of polices under asymmetric information began in the 1960s and 1970s (Arrow (1963), Pauly (1974), Rothschild & Stiglitz (1976)), by which time the adverse consequences of information asymmetry had already been widely accepted. However, empirical test results of its presence are mixed and varied by markets.

Arguably from society's viewpoint, the high risks are those who most need insurance. That is, if the social purpose of insurance is to compensate the population's losses, then insuring high risks contributes more to this purpose than insuring low risks. In this case, restriction on risk classification may be reasonable, otherwise premium for high risks would be too high to be affordable. Thus, the traditional insurers' risk classification practices might be considered as contrary to this social purpose.

To highlight this issue, ''loss coverage'' was introduced in Thomas (2008) as the expected population losses compensated by insurance. A higher loss coverage indicates that a higher proportion of the population's expected losses can be compensated by insurance. This might be a good result for the population as a whole. A corollary of this concept is that, from a public policy perspective, adverse selection might not always be a bad thing. The author argued that a moderate degree of adverse selection could be negated by the positive influence of loss coverage. Therefore, when analysing the impact of restricting insurance risk classification, loss coverage might be a better measure than adverse selection.

In this thesis, we model the outcome in an insurance market where a pooled premium is charged as a result of an absence of risk-classification. The outcome is characterised by four quantities: equilibrium premium, adverse selection, loss coverage and social welfare. Social welfare is defined as the total expected utility of individuals (including those who buy insurance and those who do not buy insurance) at a given premium. Using a general family of demand functions (of which iso-elastic demand and negative-exponential demand are examples) with a non-decreasing demand elasticity function with respect to premium, we first analyse the case when low and high risk-groups have the same constant demand elasticity. Then we generalise the results to the case where demand elasticities could be different.

In general, equilibrium premium and adverse selection increase monotonically with demand elasticity, but loss coverage first increases and then decreases. The results are consistent with the ideas proposed by Thomas (2008, 2009) that loss coverage will be increased if a moderate degree of adverse selection is tolerated. Furthermore, we are able to show that, for iso-elastic demand with equal demand elasticities for high and low risks, social welfare moves in the same direction as loss coverage, i.e. social welfare at pooled premium is higher than at risk-differentiated premiums, when demand elasticity is less than 1. Therefore, we argue that loss coverage may be a better measure than adverse selection to quantify the impact of risk classification scheme being restricted. Moreover, (observable) loss coverage could also be a useful proxy for social welfare, which depends on unobservable utility functions. Therefore, adverse election is not always a bad thing, if demand elasticity is sufficiently low.

The research findings should add to the wider public policy debate on these issues and provide necessary research insights for informed decision making by actuaries, regulators, policyholders, insurers, policy-makers, capital providers and other stakeholders.