Best bounds for expected financial payoffs I algorithmic evaluation

A systematic approach to the evaluation of best bounds for expected financial payoffs, in case the mean, variance and range of the distribution are known, is presented. It is based on the majorant/minorant mathematical technique, which consists to bound a payoff by some quadratic polynomial. For the class of piecewise linear payoff functions, a classification of the global triatomic extrema is given, and a general algorithm for evaluation is formulated.