So it occurs to me that, in my last post, I left one important question unanswered: what, in fact, is an actuary? What do they do, and why is it considered a remotely sensible use of time?
Actuarial science is best considered as forward-looking accounting. Traditional accountants look at what has happened in the past and try to figure out whether a company is broke or not. Actuaries look at what is likely to happen in the future and try to figure out whether a company will survive it all...
An example. Let's say that you send a ship to India to pick up some tea. You want to be sure that you don't go broke if the ship sinks. So you buy an insurance policy.
The company who sells you the policy has a dilemma: how much do they charge? If they charge too little for their policies then, in the long run, too many ships will sink and they'll go bust. If they charge too much, their competitors will steal all their trade. By this point, their stockholders are probably breathing down their neck for proof that the company is doing the right thing.
How do they handle this situation? They ask an actuary. The actuary will look through the mathematical literature on ship failures, consider the specific situation, and propose an actuarial model: a set of formulae that will put a price on that policy. The model may handle a number of factors - expected weather conditions at this time of year, age of ship, amount of maintenance done, even the professional opinion of engineers paid to examine the ship. The goal is to calculate a figure that will keep the company's "risk of ruin" - their chance of going bankrupt - below a certain level.
The three main areas of actuarial work are:
1) General insurance - dealing with the risk of expensive stuff breaking
2) Life insurance/assurance - dealing with the risk of people breaking
3) Pensions - dealing with the risk of people staying alive long after they've stopped earning
I mainly work in pensions, where the problem we deal with is that we don't know when someone will die. There are two different approaches to dealing with this:
1) Defined contribution schemes. These schemes hold a specified investment portfolio for each policyholder (PH), normally linked to the amount of money that the PH has fed into the scheme over the years. If, ten years down the line, all the scheme's investments fail, the PH just doesn't get much money. The hard part, then, is projecting the policy's value at date of redemption.
2) Defined benefit schemes. These set out in advance, according to some horrible messy formula, precisely how much money a pensioner will get. The hard part, then, is figuring out the amount of money the scheme needs to have right now in order to pay for all this. This is called scheme valuation and it is the subject of much actuarial thought, and of the heavy-duty actuarial software described in the last post.
In general, companies don't like DB schemes because, if the scheme's portfolio fails, the company has to carry the can. This is hard to allow for unless you have an unlimited source of money. So companies prefer DC schemes.
By contrast, governments are perfectly happy with DB schemes. After all, if the scheme needs more money, they'll just raise taxes. And having a deterministic formula for benefits makes negotiation with unions easier. In the UK, I suspect that this rather blasé attitude is likely to backfire at some point when the public realises how good the benefits are in the public sector...