Fundamental Theorems of Asset Pricing for Good Deal Bounds

21 Pages Posted: 6 May 2004

See all articles by Jeremy Staum

Jeremy Staum

Northwestern University - Department of Industrial Engineering and Management Sciences

Abstract

We prove fundamental theorems of asset pricing for good deal bounds in incomplete markets. These theorems relate arbitrage-freedom and uniqueness of prices for over-the-counter derivatives to existence and uniqueness of a pricing kernel that is consistent with market prices and the acceptance set of good deals. They are proved using duality of convex optimization in locally convex linear topological spaces. The concepts investigated are closely related to convex and coherent risk measures, exact functionals, and coherent lower previsions in the theory of imprecise probabilities.

Keywords: Asset pricing, coherent risk measure, convex risk measure, equivalent martingale measure, fundamental theorem, good deal bounds, imprecise probabilities, incomplete markets

Suggested Citation

Staum, Jeremy, Fundamental Theorems of Asset Pricing for Good Deal Bounds. Mathematical Finance, Vol. 14, No. 2, pp. 141-161, April 2004. Available at SSRN: https://ssrn.com/abstract=522028

Jeremy Staum (Contact Author)

Northwestern University - Department of Industrial Engineering and Management Sciences ( email )

2145 N. Sheridan Road
Evanston, IL 60208-3119
United States

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