In 1738, Daniel, trying to solve a problem in probability theory and the theory of gambling by use of the calculus, stumbled on the concept of the law of diminishing marginal utility of money.
Assuming only a basic knowledge ofprobability and calculus, it covers the material in a mathematically rigorous and complete way at a level accessible to second or third year undergraduate students.
Large deviation theory provides a good method to calculus the probabilityof rare event, which will have great impact once it happens although its probability may be very small.