Relativities in Financial Markets

21 Pages Posted: 15 Feb 2016

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: February 15, 2016

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.

Keywords: non-additive probability; acceptable risks; nonlinear martingales; nonlinear expectation; measure distortions

JEL Classification: G10, G11, G13

Suggested Citation

Madan, Dilip B., Relativities in Financial Markets (February 15, 2016). Robert H. Smith School Research Paper No. RHS 2732825, Available at SSRN: https://ssrn.com/abstract=2732825 or http://dx.doi.org/10.2139/ssrn.2732825

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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