Fire Insurance (1851-1880)
In the UK, fire insurance first emerged as a significant commercial activity in London in the decades following the Great Fire of 1666. A century later, it was well-established across the country, and increasingly covered industrial and agricultural fire risks as well as residential properties and retailers. By the nineteenth century, some of the leading British fire insurance companies had become successful multinationals, writing substantial business in North America and the British colonies.
Eighteenth- and nineteenth-century fire insurance practices did not make use of the statistical methods that were being contemporaneously developed and successfully applied in life assurance. The broad challenges of applying statistical and analytical techniques to general insurance were wholly applicable to fire insurance business: the classification of historical claims experience into homogenous groups; the modelling of claim size as well as claim frequency; making allowance for social effects such as fraud and its propensity to vary with the prevailing economic climate. These challenges led to a deep scepticism of the potential usefulness of statistical analysis of historical experience as an alternative to underwriting by case-by-case estimation.
However, some of the pioneering actuaries of the mid-nineteenth century were attracted to the challenge. Samuel Brown, who would go on to become the third President of the Institute, and who wrote one of the first actuarial papers on investment, also wrote one of the first actuarial papers on general insurance. The mid-nineteenth-century challenges in developing statistical analysis of fire insurance started with a lack of available data on historical claims experience. The pooling of life assurers’ mortality data was a well-established practice by the mid-nineteenth century but fire insurers showed no inclination to follow that collaborative practice. This was both due to commercial sensitivities and because the insurers recognised that their data records were generally inadequate for this purpose. Brown encouraged the fire offices to cooperate on the development of statistical claims analysis by providing him with historical data that he would pool but he found ‘the course of his investigations on this subject was stopped by the determination expressed by the fire offices to refuse him all information whatever’.
Brown struck upon an alternative rich source of data. The fire offices had formed the London Fire Engine Establishment in the 1830s to protect its insured properties. Its superintendent, Mr Baddeley, compiled comprehensive records of every fire to which its fire engines were called. These records included the extent of damage to the property, the occupations of the premises, the cause of the fire, and what proportion of the value of the building was insured. Brown’s 1851 paper presented a tabulation and analysis of Baddeley’s records for the years 1833 to 1849. Baddeley’s records, however, could only tell half the story. In order to deduce some useful insights for fire insurance premium-setting, some measure of the ‘exposed-to-risk’ was also required. For this purpose, Brown turned to the Post Office Directory, which provided an estimate of the total number of buildings that lay within the area covered by London Fire Engine Establishment and, for commercial properties, the trades undertaken at the premises.
Armed with these estimates of the number of buildings exposed and the historical fire experience, Brown then calculated the one-year probabilities of fire for commercial properties as a function of the occupation undertaken in the property. He estimated, for example, that there was a 0.34 % probability of fire in a given year at a grocers’ premises, whereas the corresponding probability for Lucifer match-makers was a rather disconcerting 30 %. By observing the distribution of the damage categories recorded by Baddeley, and making some assumptions about the cost associated with each degree of damage, he calculated the premium rates required for each class of occupation. His calculations implied an average annual premium rate of around 5 % of sum insured with significant variation by use of premises.
Brown himself recognised how the inherent complexity of fire insurance business inevitably placed significant limitations on the usefulness of his premium rate estimates:
The locality, the construction of the buildings, the distance from a fire engine station, and, still more, the manner in which an adjoining building may be injured by a fire breaking out in a neighbour’s house, would have to be considered.
Nonetheless, he had made resourceful and practical use of whatever limited data was available, and had handled it competently to provide some illuminating insights and new quantitative reference points for insurance premium-setting.
Thomas Miller wrote two short papers on the application of statistical techniques to fire insurance that appeared in the Journal of the Institute of Actuaries in 1857 and 1880. Unlike in life assurance, the claim size in the event of a general insurance claim is usually not a fixed amount. Assumptions are therefore required about the behaviour of claim size as well as claim frequency. In the case of fire insurance, the claim size would be based on the cost of the fire damage incurred, up to the size of the policy’s sum insured. Furthermore, fire insurance policies could insure either the full value of the property or a specified sum that was only a fraction of the value of the property.
Miller’s first paper considered some of the difficulties in interpretation of claim experience that resulted from these features of fire insurance. He argued that fire insurance claim data would be more useful if it reported the size of loss as a proportion of the value of the property rather than the usual practice of recording it as a proportion of the sum insured. This would allow the behaviour of claim size and hence insurance cost to be better understood as a function of how the sum insured varied as a proportion of property value. He argued that the profitability of the fire office and the adequacy of its premium bases should be analysed not by considering the actual profits that had been generated by the business, but by considering what the profits would have been if the size of all its policies was standardised to the same sums insured. This would remove the impact of the variation in policy size that occurred due only to the incidental preferences of a particular group of policyholders— ‘accidental circumstances’ that were not controlled or targeted by the insurer. This could be considered as an early example of actuarial thinking on the analysis of surplus.
Miller’s second paper considered what the appropriate unit of risk exposure should be for fire insurance. He suggested it should be based on the number of building floors insured rather than simply the number of buildings. He then developed an algebraic framework for calculating fire probabilities based on the two possible ways of a floor catching fire: by a fire originating on that floor; and by a fire spreading to the floor from another floor. This allowed him to produce probabilities of fire for a given floor of a building as a function of the total number of floors in that building. From this he produced the result that the probability of a given building floor catching fire increased with the number of floors in the building. Miller produced some numerical examples of his algebra, but made no attempt to calibrate his model to empirical data. It is hard to believe that fire insurance practitioners would have recognised any practical value in his approach.
These early actuarial contributions had little to no impact on British fire insurance practice. In 1878, the historian and actuary Cornelius Walford noted in a Journal paper, ‘It will no doubt be thought remarkable that, after two centuries of experience, the rates of fire insurance are still deduced by a method entirely ‘non-scientific’ ... But if there be no scientific base for fire insurance premiums, it is not from the want of suggestions in this direction [from actuaries].’
British actuarial interest in fire insurance and property insurance subsequently waned. No paper of note on fire or property insurance was published in the Journal or Transactions between Miller’s 1880 paper and the end of the Second World War.