An Isomorphism Between Asset Pricing Models With and Without Linear Habit Formation

We show an isomorphism between optimal portfolio selection orcompetitive equilibrium models with utilities incorporatinglinear habit formation, and corresponding models without habitformation. The isomorphism can be used to mechanically transformknown solutions not involving habit formation to correspondingsolutions with habit formation. For example, the Constantinides(1990) and Ingersoll (1992) solutions are mechanically obtainedfrom the familiar Merton solutions for the additive utilitycase, without recourse to a Bellman equation or first-orderconditions. More generally, recent solutions to portfolio selectionproblems with recursive utility and a stochastic investmentopportunity set are readily transformed to novel solutions ofcorresponding problems with utility that combines recursivitywith habit formation. The methodology also applies in the contextof Hindy–Huang–Kreps (1992) preferences, where ourisomorphism shows that the solution obtained by Hindy and Huang(1993) can be mechanically transformed to Dybvig's (1995) solutionto the optimal consumption-investment problem with consumptionratcheting.     

A term structure model with preferences for the timing of resolution of uncertainty

Summary In this paper we present a model of the term structure of interest rates with imperfect information and stochastic differential utility, a form of non-additive recursive utility. A principal feature of recursive utility, that distinguishes it from time-separable expected utility, is its dependence on the timing of resolution of uncertainty. In our model, we parametrize the nonlinearity of recursive utility in a way that corresponds to preferences for the timing of resolution. This way we show explicitly the dependence of prices on the rate of information, as a consequence of the nature of utilities. State prices and the term structure of interest rates are obtained in closed form, and are shown to have a form in which derivative asset pricing is tractable. Comparative statics relating to the dependence of the term structure on the rate of information are also discussed.We thank Bob Hodrick and Matt Jackson for their comments. Darrell Duffie is grateful for support from the National Science Foundation under NSF SBR-9409567. This paper presents the first model of an earlier, preliminary working paper titled: Two models of price dependence on the timing of resolution of uncertainty.     

Rationalizable Trade

We formulate necessary and sufficient conditions for interim rationalizable trade between two players. Journal of Economic Literature Classification Numbers: D82, C72.     

Recursive utility and preferences for information

Summary. This paper presents an axiomatic foundation for recursive utility that captures the role of the timing of resolution of uncertainty without relying on exogenously specified objective beliefs. Two main representation results are proved. In the first one, future utility enters the recursion through the type of general aggregators considered in Skiadas (1997a), and as a result the formulation is purely ordinal and free of any probabilities. In the second representation these aggregators are conditional expectations relative to subjective beliefs. A new recursive representation incorporating disappointment aversion is also suggested. The main methodological innovation of the paper derives from the fact that the basic objects of choice are taken to be pairs of state-contingent consumption plans and information filtrations, rather than the temporal (objective) lotteries of the existing literature. It is shown that this approach has the additional benefit of being directly applicable to the continuous-time version of recursive utility developed by Duffie and Epstein (1992). Received: February 18, 1997; revised version: July 18, 1997     

On the uniqueness of fully informative rational expectations equilibria

Summary. This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as rn-REE. Examples of quasi-complete economies include the type of economies for which demand aggregation in the sense of Gorman is possible (with or without asymmetric information), the setting of the Milgrom and Stokey no-trade theorem, an economy giving rise to the CAPM with asymmetric information but no normality assumptions, the simple exponential-normal model of Grossman (1976), and a case of no aggregate endowment risk. In the common-knowledge context, we provide necessary and sufficient conditions for a common knowledge posterior estimate, given common priors, to coincide with the full communication posterior estimate. Received: May 29, 1997; revised version: July 18, 1997     

OPTIMALITY AND STATE PRICING IN CONSTRAINED FINANCIAL MARKETS WITH RECURSIVE UTILITY UNDER CONTINUOUS AND DISCONTINUOUS INFORMATION

We study marginal pricing and optimality conditions for an agent maximizing generalized recursive utility in a financial market with information generated by Brownian motion and marked point processes. The setting allows for convex trading constraints, non-tradable income, and non-linear wealth dynamics. We show that the FBSDE system of the general optimality conditions reduces to a single BSDE under translation or scale invariance assumptions, and we identify tractable applications based on quadratic BSDEs. An appendix relates the main optimality conditions to duality.