A constrained optimization model of risky decisions

A decision model is formulated for individual choices between gambles whose probabilities and payoffs are explicitly stated. The decision situation is characterized as R_N = (X, P, Z, T, α) where X is a payoff matrix, P is the objective probability distribution over the states of nature, Z is a class of objective functions, T is tolerable regret and 1 ? α is the maximum probability for accepting regrets greater than T. Given R_N, the problem of selecting a strategy is the solution of a chance constrained optimization problem. The solutions for choice situations having two alternatives and n states of nature are developed in a series of theorems. Some implications for experimentation and possible applications are discussed.