Relativities in Financial Markets

Abstract

No arbitrage for two price economies with no locally risk free asset implies that suitably deflated prices are nonlinear martingales. However, both the deflating process and the measure change depend on the process being deflated. Further assumptions allow the nonlinear martingales in discrete time to become expectations with respect to a nonadditive probability. Such nonlinear expectations that distort probabilities are imminently reasonable given the lack of experience with tail events on both sides of the gain loss spectrum. Continuous time extensions replace probability distortions with measure distortions that distort the arrival rates of jumps. The general valuation of economic activities and the leveraging of stability in deflated price processes is then addressed. Applications include the pricing of options on relativities and the asset pricing theory for relativities in a limiting stationary state.