Stochastic Programming Tutorial for Financial Decision Making (The Saddle Property of Optimal Profits)

The complexity of the interaction between time and uncertainty made finance models to one of the most important applications of probability theory and optimization theory. Stochastic programming combines those two fields with the intention to design methodologies for planning under uncertainty. This tutorial consists of two parts, written for practitioners, in particular financial decision makers. It is to provide insights into the basic ideas of stochastic programming in an easily understandable way. This paper reveals various decision structures of investors and evaluates the profits achieved by admissible decisions. Criteria are presented which help identify the optimality of admissible decisions. Further, the optimal profit function is introduced to measure the sensitivity of optimal portfolios with respect to changes in income and term structure. In particular, the saddle property of the optimal profit function is verified with respect to different income and interest rate scenarios. This part concludes with a discussion on the stability of the optimal decisions and the usage of sensitivity results for analyzing the stochastic data with respect to the underlying investor's decision structure.