An actuary is a person who works with complex mathematical models to try and predict the likelihood of future events. An actuary is particularly important for the insurance industry. An actuary looks at the average propensity for disastrous events to occur and uses these percentages to try and predict a fair price to set insurance premiums
These predictions take into account observed trends like death rates, crime rates. They will try to break down statistics into different groups, enabling different premiums to be set for different groups of consumers. For example, non smokers may get lower health premiums. Young male drivers are statistically more likely to be involved in a car crash so car insurance will be more expensive.
Difficulties of being an actuary
Sometimes events are very difficult to predict and past trends are not always a good guide to the future. For example, global warming could well increase the likely hood of adverse weather conditions.
Moral Hazard. It is argued that the probability of certain events can change if people get insurance. For example, if you insure your bike, you have less incentive to lock it up and prevent it getting stolen.