Annuities are the annual pension that many people buy with their private pension pots when they retire.
The FSA will look at whether or not people are given enough information about the various options available. There have long been worries that many consumers may be getting a bad deal.
The FSA will look into whether insurers are doing enough to encourage pension savers to exercise 'open market option' at retirement - the right to take their savings and shop around for the best annuity.
At present, six out of 10 savers choose to accept the annuity offered by their pension provider. The difference between the best and default annuity rates could mean a £100,000 retirement pot buys an annual pension of £5,700 rather than £4,700.
The review of the market by the FSA could take up to 12 months and could lead to it 'naming and shaming' firms which are offering poor deals to savers or those that are seen as putting barriers in the way of people looking to exercise the open market option.
The National Association of Pension Funds (NAPF) has welcomed the investigation. Its chief executive, Joanne Segars, said: "The FSA is right to launch this investigation into annuities.
"Greater transparency in this market is essential if people are to have faith in pensions.
"People need to know that they can turn their pension pots into good retirement incomes when they purchase an annuity. At the moment, consumers are dealing with an unfair and opaque system that is preventing too many of them from securing a decent income for their old age."
Tom McPhail, of annuity firm Hargreaves Lansdown, pointed out that insurers have been obliged since 2002 to draw their customers' attention to the fact that they can shop around for an annuity at the point of retirement.
"The ABI code of conduct is a big step forward, however it is flawed in that it could result in insurers performing a very limited shopping around process for their customers.
"This could result in investors getting a slightly better deal than they would have done in the past, but still not as good a deal as if they shopped around the whole market.
He added: "Hopefully the FSA review will determine whether the ABI code of conduct is acting effectively to improve consumer outcomes."
