Empirical Estimates in Economic and Financial Problems via Heavy Tails

Optimization problems depending on a probability measure correspond to many economic and financial applications. Complete knowledge of this measure is necessary to solve exactly these problems. Since this condition is fulfilled only seldom, the problem has to be usually solved on the data basis to obtain satistical estimates of an optimal value and optimal solutions. Great effort has been paid to investigate properties of these estimates; first under assumptions of disribution with thin tails and linear dependence on the probability measure. Recently, it has appeared an investigation in the case of nonlinear dependence on the probability measure and heavy tailed distributions with shape parameter greater two. We focus on the case of the stable and Pareto distributions with a shape parameter in the inteval (1, 2)