Benchmarking in two price financial markets

No arbitrage for two price economies with no locally risk free asset implies that suitably benchmarked prices are nonlinear martingales. However, both the benchmarking asset and the measure change depend on the process being benchmarked. Further assumptions allow the nonlinear martingales in discrete time to become expectations with respect to a nonadditivity probability. Such nonlinear expectations are imminently reasonable given the lack of experience with tail events on both sides of the gain loss spectrum. Continuous time extensions employ measure distortions. The general valuation of economic activities and the leveraging of stability in benchmarked price processes is then addressed. Traditional asset pricing questions and investigations are then reopened for benchmarked prices. In particular, the analytics for benchmarked option pricing and the asset pricing theory for benchmarked prices in a limiting stationary state are developed. © 2016, Springer-Verlag Berlin Heidelberg.