DUALITY AND EQUILIBRIUM PRICES IN ECONOMICS OF UNCERTAINTY

Abstract

Abstract. A random variable (RV) X is given a minimum selling price (S) SU (X) := sup x {x + EU (X − x)} and a maximum buying price where U (·) and P (·) are appropriate functions. These prices are derived from considerations of stochastic optimization with recourse, and are called recourse certainty equivalents (RCE's) of X. Both RCE's compute the "value" of a RV as an optimization problem, and both problems (S) and (B) have meaningful dual problems, stated in terms of the Csiszár φ-divergence qi φ pi qi a generalized entropy function, measuring the distance between RV's with probability vectors p and q. The RCE SU was introduced i