This article is part of a series celebrating the 20th birthday of the Isaac Newton Institute in Cambridge. The Institute is a place where leading mathematicians from around the world can come together for weeks or months at a time to indulge in what they like doing best: thinking about maths and exchanging ideas without the distractions and duties that come with their normal working lives. And as you'll see in our articles, what starts out as abstract mathematics scribbled on the back of a napkin can have a major impact in the real world.

Many people's impression of mathematics is that it is an ancient edifice built on centuries of research. However, modern quantitative finance, an area of mathematics with such a great impact on all our lives, is just a few decades old. The Isaac Newton Institute quickly recognised its importance and has already run two seminal programmes, in 1995 and 2005, supporting research in the field of mathematical finance.

"Quantitative finance is a fairly new area of mathematics," says David Hobson, one of the organisers of the Developments in Quantitative Finance programme which ran in 2005. "It didn't exist before the early 1980s and few academics classed themselves primarily as researchers in mathematical finance until about fifteen years ago." Researchers were experts in other types of mathematics – such as probability theory, stochastic modelling, functional analysis and numerical analysis, before moving into mathematical finance.

Bringing together the City and the ivory tower

"One of the ways the programme was successful was in getting industry and academia together," says Hobson. "Research in mathematical finance is undertaken in both universities and in banks. But banks are very proprietorial about their research and reluctant to share what they've done as they think they will lose an advantage." The programme gave credibility to industry researchers who talked about their research, allowing them to be seen as experts in that area, which is, in itself, attractive to potential clients.

This interaction was of great benefit to the academic researchers also. "It gave academics a route into what banks are really interested in. Otherwise there is a tendency to think about interesting mathematical questions but not important practical questions," says Hobson.

It was this aspect of bringing together so many people from industry and academia that makes this programme stand out. The programme had 55 long-stay and 153 short-stay participants. It was, and still is, the largest programme held at the Institute in terms of number of participants. "Nearly everybody who was anybody in mathematical finance passed through Cambridge during those six months," says Hobson. "The Newton Institute is unique. No other institute runs programmes at the same scale as the Newton Institute. This was the biggest long-term event in mathematical finance that I'm aware of."

Pensions modelling

The programme not only brought together academics and industry, it was also an important opportunity for the fields within mathematical finance to come together. Finance has two mathematically separate industries: investment banking and the insurance and pensions industry. Historically, actuaries in the pensions industry have been conservative in using sophisticated mathematics. However, the current debate regarding pensions may result in more advanced mathematical models being utilised.

"On average people are living longer than they used to – that's nice for us but it's causing problems in funding pensions," says programme participant Andrew Cairns. At the time of the programme he was trying to model how the cost of pensions might change in the future and how much uncertainty there was in those projections. The programme, says Cairns, gave him time to think more deeply about serious problems. He was also able to make presentations on his work and receive feedback from his assembled colleagues. "It certainly helped to get feedback on that research, and I would not have got that if I hadn't been participating in the programme."

One of his papers, the main part of which was written during his stay at the Institute, has been very influential and this research is now the basis for work in collaboration with the pensions industry. "On the back of that paper there has been a lot of interest from the pensions industry. Since then my collaborators and I have been working with JP Morgan: firstly to educate the people buying pension funds, and secondly to work with the banks and other financial services to manage that particular risk."

The simplest example of how this risk is managed in practice is something called a longevity swap. Essentially the pension fund swaps the payments to its pensioners (which would carry on as long as they lived) for a fixed set of payments with a third party, that is acting essentially as an insurer. "There is a price to pay for that but some pension funds are willing to pay a premium to get greater certainty over their future costs." Cairns has been working with JP Morgan on a set of mathematical models, called LifeMetrics, which are actively being used by the industry. This is a new and growing market. The value of longevity swap deals already traded in the UK market is estimated to be well over £10billion by the end of 2010.

Looking to the future

"In a new area things advance rapidly," says Hobson. Questions that were important in the 1995 programme, such as modelling interest rates, were already well understood by the 2005 programme and new questions were the focus of research. Quantitative finance is an exciting and fast moving research area, and it is also very influential on the finance industry and society as a whole.

The 2005 programme, as well as the global credit crisis that began in 2008, made one thing very clear: more communication between academia and the finance industry is needed if sophisticated mathematical techniques are going to be used successfully in the markets.

"The real problem in the credit crisis was a lack of understanding and communication of assumptions and limitations of the models," says programme participant Andrew Cairns. "The onus is now on the banks and those that regulate them to have people who can understand the language of the mathematicians at all levels, in order for them to understand the risks."