This supplementary Technical Appendix contains formal proofs of the propositions which are stated in Anyfantaki, S., S. Arvanitis, S., Th. Post, Th. and N. Topaloglou, 2019, 'Stochastic Bounds for Portfolio Analysis', available at SSRN:"https://ssrn.com/abstract=3181869 "...

Starting from the reward-risk model for portfolio selection introduced in De Giorgi (2004), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. The reward-risk portfolio selection arises froman axiomatic definition of reward and risk...

This study develops and implements a theory and method for analyzing whether introducing new securities or relaxing investment constraints improves the investment opportunity set for risk averse investors. We develop a test procedure for ‘stochastic spanning’ for two nested polyhedral...