The Theory of Good-Deal Pricing in Financial Markets

Abstract

In this paper the term "good-deal pricing" stands for any pricing technique based on the absence of attractive investment opportunities - good deals - in equilibrium. The theory presented here shows that any such technique can be seen as a generalization of no-arbitrage pricing and that, with a little bit of care, it will contain the no-arbitrage and the representative agent equilibrium as the two opposite ends of a spectrum of possible no-good-deal equilibrium restrictions. We formulate the Extension and the Pricing Theorem in no-good-deal framework and establish general properties of no-good-deal price bounds determined by von Neumann-Morgenstern preferences. Our theory provides common footing to a range of applications, such as Bernardo and Ledoit (2000), Cerny (1999), Cochrane and Saá-Requejo (2000), and Hodges (1998).

Keywords: arbitrage, good deal, virtually desirable claim, state price functional, incomplete market, reward for risk measure, Generalized Sharpe Ratio, admissible price region, equivalent martingale measure

JEL Classification: G12, D40