Uncertainty about future returns on financial assets is the essence of the modelling of financial markets. An excellent introduction to this area is contained in the two 2003 Nobel lectures by Robert Engle (2004) and Clive Granger (2004). 2  BIS Review 73/2004  death.5 Collective risk - that average expectation of life will rise or fall in the future - cannot, by definition, be shared among members of the same generation. The principle of insuring individual longevity risk is that those who live longer than average can be paid using the contributions of those who die earlier than average. But if the average itself rises all contributions must increase - there is no possibility for insuring changes in the average from within the cohort. Can we quantify this risk? The expectation of life has risen significantly over the past century. But how will it change in the future? To answer that question we need to model and quantify longevity risk. 3. Modelling and quantifying risks  Quantitative modelling has been one of the great advances of the social sciences over the past fifty years. But forecasts, whether of longevity or any other economic or social variable, inevitably require a judgment about how far the past can inform us about the future. Projecting longevity is fraught with difficulty.
Chart 8 constructs a fan chart for female life expectancy at birth in the United Kingdom derived from the latest forecast published by the Government Actuary’s Department. The width of the fan chart shows how forecasts of life expectancy are likely to change in the future, as new information and ideas about mortality evolve,  12  To understand the concept of independence consider the example of a church spire that is struck by lightning several times. Is this just coincidence (implied by the assumption that the strikes are independent of each other) or does the spire have certain characteristics that lead it to be struck regularly? Given our knowledge of spires and lightening the latter is more plausible. Similarly, there may be characteristics, genetic or other, and still largely unknown, that make particular families more likely to experience cot deaths than others. 13  Hill (2002) and (2004). See also Dawid (2004) and Eggleston (1978) for a discussion of the difficulties courts find with the concepts of conditional probability and Bayes’ theorem. 14  The forecast for inflation is based on the assumption that interest rates follow the path expected by financial markets over an average of the fifteen days prior to the finalisation of the Inflation report. 6  BIS Review 73/2004  causing forecasts to be revised - assuming that news about life expectancy arrives in the future at about the same rate as in the past.