Two remarks on the uniqueness of equilibria in the CAPM

Sunspot equilibria and the transfer paradox

“…Computable general equilibrium models (cf. Shoven and Whalley (1992)), examples for the occurrence of the transfer paradox (Leontief (1936), Chichilniski (1980), Chichilniski (1983), Rao (1992), Geanakoplos and Heal (1983), etc), and examples for multiple equilibria (Kehoe (1985), Kehoe (1991), Hens, Schmedders and Voß (1999), Hens, Laitenberger and Löffler (2002)) therefore use the class of CES-utility functions. The class of utility functions assumed in this paper (concave transformations of additively separable functions) includes CES-functions.…”

The two-fund separation theorem revisited

“…Recently Böhm and Chiarella (2005) investigated a dynamic intertemporal extension of the CAPM which is founded on a modern formulation of the two-fund separation theorem (Lemma 2.3) and an existence result of intertemporal CAPM equilibria (Lemma 2.5) which is based on Dana (1999) and Hens et al (2002). For the proofs of these two lemmas the reader is referred to Böhm (2002).…”

“…On the contrary, if one of the investors has finite limiting slopes, then an asset-market equilibrium exists for any possible market portfolio because at least one investor is willing to take on an infinite amount of risk for a finite price. The role of this limiting condition seems to have been overlooked in Nielsen (1987), Dana (1999), Hens et al (2002), and Böhm and Chiarella (2005) This work arose from a survey article Wenzelburger (2009) prepared for Hens and Schenk-Hoppé (2009). Its main purpose is to provide an elementary, complete and self-contained proof of the two-fund separation theorem for mean-standard deviation utility functions of the form U (µ, σ ) and arbitrary probability distributions for future returns.…”

Existence of Sunspot Equilibria and Uniqueness of Spot Market Equilibria: The Case of Intrinsically Complete Markets

“…Those changes in risk aversion are know to be very important for asset demand. See the related papers by [20,21,15] and also the monograph by [10] for an extensive study.…”

“…Computable general equilibrium models (cf. [35]), examples for the occurrence of the transfer paradox ( [27,6,7,34,14], etc), and examples for multiple equilibria ( [24,25,20,21]) therefore use the class of CES-utility functions. The class of utility functions assumed in this paper (monotonic transformations of additively separable functions) includes CES-functions.…”