Brief History
The first rigorous results concerning large deviations are due to the Swedish mathematician Harald Cramér, who applied them to model the insurance business. From the point of view of an insurance company, the earning is at a constant rate per month (the monthly premium) but the claims come randomly. For the company to be successful over a certain period of time (preferably many months), the total earning should exceed the total claim. Thus to estimate the premium you have to ask the following question : "What should we choose as the premium such that over months the total claim should be less than ? " This is clearly the same question asked by the large deviations theory. Cramér gave a solution to this question for i.i.d. random variables, where the rate function is expressed as a power series.
A very incomplete list of mathematicians who have made important advances would include Petrov, Sanov, S.R.S. Varadhan (who has won the Abel prize), D. Ruelle and O.E. Lanford.
Read more about this topic: Large Deviations Theory
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