The Surplus Process As A Fair Game -- Utilitywise

The concept of utility is twofold. One may think of utility: I) as a tool to describe a "fair game" 2) as a quantity that ought to be maximized. The first line of thought was initiated by Daniel Bernoulli in connection with the St. Petersburg Paradox. In recent decades, actuaries, economists, operations researchers and statisticians (this order is alphabetical) have been concerned mostly with optimization problems, which belong to the second category. Most of the actuarial models can be found in a paper by Botch [4] as well as in the texts by Beard, Personnel and Pentikainen [3], Buhlmann [6], Seal [I5], and Wolff [17].