Abstract This paper studies arbitrage-free financial markets with bid-ask spreads whose super-hedging prices are submodular. The submodular assumption on the price, or supermodularity usually assumed utility functions, is formal expression of perfect complementarity, which dates back to Fisher, Pareto, and Edgeworth, according Samuelson (J Econ Lit 12:1255–1289, 1974). Our main contribution pro...

Throughout the course of history, annexation has littered international scene as major powers exert their force in takeover smaller lands. Sometimes these takeovers are violent and others not, but what we undoubtably see is that will be successful if economic indicators rise, post-acquisition. We focus our attention to three prominent cases by powers: Crimea, Kashmir Hong Kong. briefly examine ...