How does perturbation analysis work in finance and economics?

In this paper, we summarize and report the results that demonstrate how the perturbation analysis (PA), which was originally developed for discrete event dynamic systems, can be applied to obtain interesting results in financial engineering and economic problems where both time and states are continuous and dynamic programming fails. We study the "irrational" behavior of human preference over random outcomes, modeled by distorting the probability of the events. Efficient PA based algorithms can be developed for the optimization of potforlio with distorted performance, and analytical solution can be obtained for complete markets. In addition, the property obtained can be used to replace the independence axiom in the non-linear expected utility theory to characterize the representations.