Information theory in actuarial science

The paper deals with a branch of statistics in which optimization plays an important role. It presents the maximum entropy approach for incorporating prior information into the determination of probability distributions. First, the concept of ‘information’ and ‘uncertainty’ and their appropriate measures are introduced. Next, the maximum entropy methodology is presented in the form of a mathematical programming model, and duality statements are applied to develop the formula for its situation. Finally, the method is shown to be useful in several areas in actuarial modeling.