Strategic market games with a finite horizon and incomplete markets

Summary. We study a strategic market game associated to an intertemporal economy with a finite horizon and incomplete markets. We demonstrate that generically, for any finite number of players, every sequentially strictly individually rational and default-free stream of allocations can be approximated by a full subgame-perfect equilibrium. As a consequence, imperfect competition may Pareto-dominate perfect competition when markets are incomplete. Moreover - and this contrasts with the main message conveyed by the market games literature - there exists a large open set of initial endowments for which full subgame-perfect equilibria do not converge to -efficient allocations when the number of players tends to infinity. Finally, strategic speculative bubbles may survive at full subgame-perfect equilibria.Received: 24 January 2002, Revised: 21 February 2003, JEL Classification Numbers: C72, D43, D52. Correspondence to: Gaël GiraudWe thank Tim Van Zandt for his comments.     

The instantaneous capital market line

Summary. We show that if the intercept and slope of the instantaneous capital market line are deterministic, then investors will not hold any hedge portfolios in the sense of Merton [9, 11]. They will choose portfolios that plot on the capital market line, and they will slide up and down the capital market line over time as their wealth and risk tolerance change. This result allows us to aggregate over investors and derive a single factor CAPM where the first and second moments of security returns may change stochastically over time and markets are potentially incomplete.Received: 21 June 2004, Revised: 10 December 2004, JEL Classification Numbers: G11, G12.An earlier version of this paper was presented at the Econometric Society Meeting in Pasadena (1997) under the title “Portfolio selection and asset pricing with dynamically incomplete markets and time-varying first and second moments”.     

Pooling and endogenous market incompleteness

Summary. We study a financial market economy with a continuum of borrowers and pooling of borrowers promises. Under these conditions and in the absence of designing costs, utility-maximizing decisions of price-taking borrowers may lead to financial market incompleteness. Parametrizing equilibria through the borrowers no-arbitrage beliefs, we link expectations to the financial market structure. Markets are complete if and only if borrowers beliefs are homogeneous. Price-taking behavior causes a coordination problem which in turn yields indeterminacy and inefficiency of equilibrium allocations.Received: 29 May 2003, Revised: 13 February 2004, JEL Classification Numbers: D50, D52.Correspondence to: Alessandro CitannaWe would like to thank David Cass, John Geanakoplos, Thorsten Hens, Atsushi Kajii, and an anonymous referee for their comments. The first author also thanks CERMSEM (Paris I) and Columbia University Graduate School of Business for the hospitality. A first version of this paper has appeared as GSIA Working Paper #1997-E137, Carnegie Mellon University, which itself revised Citanna and Villanacci (1995).     

Asymptotic methods for asset market equilibrium analysis

Summary. General equilibrium analysis is difficult when asset markets are incomplete. We make the simplifying assumption that uncertainty is small and use bifurcation methods to compute Taylor series approximations for asset demand and asset market equilibrium. A computer must be used to derive these approximations since they involve large amounts of algebraic manipulation. We use this method to analyze the allocative and welfare effects of introducing a new security. We find that adding any nontrivial derivative security will raise the price of the risky security relative to the bond when risks are small. Received: April 1, 2000; revised version: January 10, 2001     

Asset prices and business cycles under market incompleteness

In this paper, we study the quantitative implications of a real business cycle model where the firm is the capital owner, households are heterogeneous, and markets are incomplete due to restricted asset trade. Since, under these assumptions, the usual firm objective is no longer well defined, several non-standard objectives are incorporated into the model. These include variants of market value maximization and a utility function for the firm. We find that the presence of market incompleteness alters little the behavior of asset returns. On the other hand, the behavior of the macroeconomic aggregates is quite sensitive to the firm objective, which affects the capital accumulation path. In contrast to conventional findings, capital is not necessarily higher when markets are incomplete. In addition, the different capital accumulation effects imply that shareholders with different asset wealth might prefer different firm objectives.     

Complete and incomplete markets with short-sale constraints

Summary. This paper argues that the introduction of a short-sale constraint in the Arrow-Radner framework invalidates standard definitions of complete and incomplete markets. Two threshold values with familiar properties arise in this constrained set-up. If short sales are not allowed on some security, then financial markets will be incomplete in the standard sense. Beyond a particular level of the short-sale bound, financial markets are “complete”, since the short-sale constraint is not effective. For intermediate bounds the distinction between complete and incomplete financial markets is blurred. Although some technical definitions hold, agents can not fully transfer wealth among states. These intermediate cases, called “technically incomplete markets”, exhibit interesting welfare properties. For instance, the resulting equilibrium allocations may not be Pareto-dominated by those of the non-restricted complete markets equilibrium. Received: November 28, 2000; / revised version: November 9, 2001     

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

Summary. We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure. Received: September 17, 1996; revised version: November 7, 1997     

New financial markets: who gains and who loses

Summary. We evaluate the effects of new financial markets in a two-period incomplete markets model with heterogenous agents. For analytical tractability, we focus on the special case where utility is exponential and risks are normally distributed. We provide a complete characterization of life-cycle consumption and portfolio choice. The effect of new financial markets on individual welfare equals the sum of what we call the portfolio effect and the price effect. The portfolio effect is proportional to the square of the difference between the average exposure to the new asset in the economy and an individual investors exposure adjusted for risk aversion. The portfolio effect is always positive and measures the improved ability of investors to transfer consumption across states. The price effect captures the effect on individual welfare of changes in asset prices. We show that new financial markets drive down the prices of all assets which raises the interest rate and thus affects the ability of investors to transfer consumption across time. The price effect is positive for net savers but can be negative for net borrowers. For net borrower households, the price effect can wipe out the portfolio effect and lead to welfare reductions.Received: 24 July 2003, Revised: 22 March 2004, JEL Classification Numbers: D31, D52, G11, G12.Paul Willen: Thanks to Viral Acharaya, Alberto Bisin, Steve Davis, John Geanakoplos and a thoughtful anonymous referee for helpful comments and suggestions. Thanks also to seminar audiences at Stanford, Berkeley and at the 2001 Stony Brook workshop on incomplete markets for comments and suggestions. I gratefully acknowledge research support from the Graduate School of Business at the University of Chicago.     

Excess price volatility and financial innovation

Summary. In a three-period finite exchange economy with incomplete financial markets and retrading, we study the effects of the degree of incompleteness and of changes in the financial structure on asset price volatility. In what are essentially no aggregate risk economies, asset price volatility is a sunspot-like phenomenon. If markets are completed by financial innovation, asset price volatility reduction is generic. With aggregate risk, changes in the financial structure affect asset price volatility through a pecuniary externality. Financial innovation which decreases equilibrium price volatility can be crafted under conditions of sufficient market incompleteness. Numerical examples illustrate the role of risk aversion for volatility changes and show that, with or without aggregate risk, reducing the degree of incompleteness per se is not necessarily associated with a volatility reduction.Received: 10 October 2003, Revised: 3 June 2004, JEL Classification Numbers: C60, D52, G10. Correspondence to: Alessandro CitannaThis research project stems from and expands previous work circulated as Financial innovation and price volatility, GSIA Working Paper #1996-E30 and Controlling price volatility through financial innovation, Kellogg Working Paper #2002-1338. We thank Herakles Polemarchakis and Chris Telmer for their comments. We are grateful to an anonymous referee for careful reviews of earlier versions. The first author thanks also GSIA - Carnegie Mellon University for the kind hospitality during Fall 2002, when part of this project was completed.     

Computable general equilibrium with financial markets

Summary. There are a wide variety of theoretical general equilibrium models with incomplete security markets. In this paper we give a general recipe for using homotopy algorithm to compute equilibria in these models. In many models, taxes, transaction-costs or other market frictions introduce the additional difficulty that equilibrium prices or choices (but not equilibrium allocations) may be undetermined. In order to demonstrate how these difficulties can be dealt with, we develop a globally convergent algorithm to compute equilibria in a model with cash-in-advance constraints, several goods and incomplete financial markets. Furthermore we describe how to implement the algorithm using a publicly available suite of subroutines for homotopy-pathfollowing. Received: October 1, 1999; revised version: December 16, 2000     

Equilibrium selection in coordination games with simultaneous play

Summary. We apply the dynamic stochastic framework proposed in recent evolutionary literature to a class of coordination games played simultaneously by the entire population. In these games payoffs, and hence best replies, are determined by a summary statistic of the population strategy profile. We demonstrate that with simultaneous play, the equilibrium selection depends crucially on how best responses to the summary statistic remain piece-wise constant. In fact, all the strict Nash equilibria in the underlying stage game can be made stochastically stable depending on how the best response mapping generates piece-wise constant best responses. Received: February 12, 2001; revised version: October 29, 2001     

Computing equilibria in finance economies with incomplete markets and transaction costs

Summary. Transaction costs on financial markets may have important consequences for volumes of trade, asset pricing, and welfare. This paper introduces an algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and transaction costs. We show that economies with transaction costs can be analyzed with differentiable homotopy techniques and thus in the same framework as frictionless economies despite the existence of non-differentiabilities of agents asset demand functions and the existence of locally non-unique equilibria. We introduce an equilibrium selection concept into the computation of economic equilibria that picks out a specific equilibrium in the presence of a continuum of equilibria.Received: 2 December 2002, Revised: 15 November 2004, JEL Classification Numbers: C61, C62, C63, C68, D52, D58, G11, G12. Correspondence to: P. Jean-Jacques HeringsThis research started when Jean-Jacques Herings enjoyed the generous hospitality of the Cowles Foundation for Research in Economics at Yale University. His research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences and a grant of the Netherlands Organisation for Scientific Research. We thank audiences at Stanford University, UC San Diego, and Venice for discussions on the subject. We are very grateful to an anonymous referee for very helpful comments on an earlier draft.     

Evolutionary stable stock markets

Summary. This paper shows that a stock market is evolutionary stable if and only if stocks are evaluated by expected relative dividends. Any other market can be invaded in the sense that there is a portfolio rule that, when introduced on the market with arbitrarily small initial wealth, increases its market share at the incumbents expense. This mutant portfolio rule changes the asset valuation in the course of time. The stochastic wealth dynamics in our evolutionary stock market model is formulated as a random dynamical system. Applying this theory, necessary and sufficient conditions are derived for the evolutionary stability of portfolio rules when relative dividend payoffs follow a stationary Markov process. These local stability conditions lead to a unique evolutionary stable portfolio rule according to which assets are evaluated by expected relative dividends (with respect to the objective probabilities).Received: 7 October 2003, Revised: 18 January 2005, JEL Classification Numbers: G11, D52, D81. Correspondence to: Klaus Reiner Schenk-HoppéWe are grateful to Jarrod Wilcox and William Ziemba for valuable comments. Financial support by the national center of competence in research Financial Valuation and Risk Management is gratefully acknowledged. The national centers in research are managed by the Swiss National Science Foundation on behalf of the federal authorities.     

Spanning with American options

In this paper, we investigate the existence of multiperiod American options generating dynamically complete markets. We show that if a primitive security separates states at the terminal date, then generically there exist multiperiod American options on that security generating dynamically complete markets. We also provide an example of an economy in which multiperiod American options on a primitive security generate dynamically complete markets, while multiperiod European options do not.     

Equilibrium in a decentralized market with adverse selection

Summary. This paper deals with trade volume and distribution of surplus in markets subject to adverse selection. In a model where two qualities of a good exist, I show that if trade is decentralized (i.e. conducted via random pairwise meetings of agents), then all units of the good are traded, and all agents have positive ex-ante expected payoffs. This feature is present regardless of the quality distribution, and persists in the limit as discounting is made negligible. This offers a sharp contrast to models of centralized trade with adverse selection (Akerlof, Wilson). Received: April 2, 2001; revised version: March 29, 2002 RID="*" ID="*" This research was funded by a grant from UQAM. I wish to thank Roberto Serrano and seminar participants at UQAM, Queen's University at Kingston, the 2001 CEME General Equilibrium Conference (Brown University), and the 2001 North American Summer Meeting of the Econometric Society (University of Maryland) for comments.     

Generic inefficiency of equilibria in the general equilibrium model with incomplete asset markets and infinite time

Summary. We consider a Lucas asset-pricing model with heterogeneous agents, exogenous labor income, and a finite number of exogenous shocks. Although agents are infinitely lived, endowments and dividends are time-invariant functions of the exogenous shock alone and are thus restricted to lie in a finite-dimensional space; genericity analysis can be conducted on sets of zero Lebesgue measure. When financial markets are incomplete, that is, there are fewer financial securities than shocks, we show that generically in individual endowments all competitive equilibria are Pareto inefficient. Received: November 22, 1999; revised version: March 4, 2002 RID="*" ID="*" We are grateful to an anonymous referee for very insightful comments on earlier drafts.     

Recursive equilibrium in endogenous growth models with incomplete markets

This paper analyzes the existence of recursive equilibria in a class of convex growth models with incomplete markets. Households have identical CRRA-preferences, production displays constant returns to scale with respect to physical and human capital, and all markets are competitive. There are aggregate productivity shocks that affect aggregate returns to physical and human capital investment (stock returns and wages), and there are idiosyncratic shocks to human capital (idiosyncratic depreciation shocks) that only affect individual human capital returns. Aggregate and idiosyncratic shocks follow a joint Markov process. Conditional on the aggregate state, idiosyncratic shocks are independently distributed over time and identically distributed across households. Finally, households have the opportunity to trade assets in zero net supply with payoffs that depend on the aggregate shock, but markets are incomplete in the sense that there are no assets with payoffs depending on idiosyncratic shocks. It is shown that there exists a recursive equilibrium for which equilibrium prices (returns) only depend on the exogenous aggregate shock variable (the wealth distribution is not a relevant state variable). Moreover, the allocation associated with this recursive equilibrium is identical to the equilibrium allocation of an economy in which households live in autarky and face both aggregate and idiosyncratic risk.I would like to thank for helpful comments Peter Howitt, Bob Lucas, Michael Magill, Tomo Nakajima, Herakles Polemarchakis, Martine Quinzii, Kevin Reffett, an anonymous referee, and seminar participants at various universities and conferences.     

Uncertainty and insurance in strategic market games

Summary. For perfectly competitive economies under uncertainty, there is a well-known equivalence between a formulation with contingent goods and one with state-specific securities followed by spot markets for goods. In this paper, I examine whether this equivalence carries over to a particular form of imperfect competition. Specifically, I look at three Shapley-Shubik strategic market games: one with contingent commodities, one with Arrow securities traded under imperfect competition and one with Arrow securities traded under perfect competition. First I compare the feasibility constraints of these three games. Then I compare their equilibrium sets. As in Peck and Shell (1989), the only common equilibria between the first and the second game are those which involve no transfer of income across states. However, if the securities markets are competitive, then the set of equilibria of the contingent commodities game and the securities game coincide. Received: June 16, 1997; revised version: April 30, 1998     

Equilibrium in a reinsurance market with short sale constraints

Summary. This paper deals with the existence of equilibrium in a dynamic reinsurance market with short sale constraints, driven by a marked point process, as studied in Bernis and Jouini (2001). We use the set of reinsurance treaties as consumption set, which is the positive orthant of some Banach lattice that can be identified to a space of martingales, . The properness of preferences is a key assumption for us to prove the existence of an equilibrium. We provide a sufficient condition for the preferences to be proper in term of loading factor of the reinsurance premium. Received: June 15, 2000; revised version: May 17, 2001     

On optimality in intergenerational risk sharing

Summary. This paper defines and studies optimality in a dynamic stochastic economy with finitely lived agents, and investigates the optimality properties of an equilibrium with or without sequentially complete markets. Various Pareto optimality concepts are considered, including interim and ex ante optimality. We show that, at an equilibrium with a productive asset (land) and sequentially complete markets, the intervention of a government may be justified, but only to improve risk sharing between generations. If markets are incomplete, constrained interim optimality is investigated in two-period lived OLG economies. We extend the optimality properties of an equilibrium with land and give conditions under which introducing a pay-as-you-go system at an equilibrium would not lead to any Pareto improvement. Received: October 5, 1998; revised version: April 3, 2001