Chapter 30 Incomplete markets

Magill, Michael; Shafer, Wayne

doi:10.1016/s1573-4382(05)80005-0

Cited by 77 publications

(69 citation statements)

References 57 publications

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“…In dynamic models with general preferences, several consumption goods and incomplete security markets an equilibrium does not always exist, and if there is one, it is typically not unique. For an overview of equilibria with incomplete markets we refer to the review articles by Geanakoplos (1990) and Magill and Shafer (1991) or the textbook by Magill and Quinzii (1996).…”

Section: Introductionmentioning

confidence: 99%

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

et al. 2016

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We provide results on the existence and uniqueness of equilibrium in dynamically incomplete financial markets in discrete time. Our framework allows for heterogeneous agents, unspanned random endowments and convex trading constraints. In the special case where all agents have preferences of the same type and all random endowments are replicable by trading in the financial market we show that a one-fund theorem holds and give an explicit expression for the equilibrium pricing kernel. If the underlying noise is generated by finitely many Bernoulli random walks, the equilibrium dynamics can be described by a system of coupled backward stochastic difference equations, which in the continuous-time limit becomes a multi-dimensional backward stochastic differential equation. If the market is complete in equilibrium, the system of equations decouples, but if not, one needs to keep track of the prices and continuation values of all agents to solve it. As an example we simulate option prices in the presence of stochastic volatility, demand pressure and short-selling constraints.JEL classification: C62, D52, D53

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Section: Introductionmentioning

confidence: 99%

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

et al. 2016

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“…The existence result is a direct consequence of a discontinuous extension of Brouwer's fixed point Theorem (1912), and is a refinement of several classical results in the standard General Equilibrium with Incomplete markets (GEI) model (e.g., Bottazzi (1995), Duffie and Shafer (1985), Husseini et al (1990), Geanakoplos and Shafer (1990), Magill and Shafer (1991)). As a by-product, we get the first existence proof of an approximated equilibrium in the GEI model, without perturbing the asset structure nor the endowments.…”

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confidence: 58%

On the existence of approximated equilibria in discontinuous economies

Bich¹

2005

Journal of Mathematical Economics

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In this paper, we prove an existence theorem for approximated equilibria in a class of discontinuous economies. The existence result is a direct consequence of a discontinuous extension of Brouwer's fixed point Theorem (1912), and is a refinement of several classical results in the standard General Equilibrium with Incomplete markets (GEI) model (e.g., Bottazzi (1995), Duffie and Shafer (1985), Husseini et al. (1990), Geanakoplos and Shafer (1990), Magill and Shafer (1991)). As a by-product, we get the first existence proof of an approximated equilibrium in the GEI model, without perturbing the asset structure nor the endowments. Our main theorem rests on a new topological structure result for the asset equilibrium space and may be of interest by itself.JEL classification : D52

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“…If C is big enough to contain the maximal feasible amount of x 0 , this contradicts consumer maximization. Thus all elements in the sequence remain bounded and the sequence converge to some σ which, using (16) and (17), is an equilibrium for the truncated economy E C .…”

Section: Consumersmentioning

confidence: 93%

“…If agents have identical preferences (a i = a, i = H, L, b), equilibrium price is 16 This implies that, 16 Accounting for corner solutions on fund portfolio decisions, the equilibrium price is An example is provided for the following parameterization. µ = 3, σ = .5, α = .8, a = 3, K = 1 .…”

Section: Appendix Bmentioning

confidence: 99%

Production and financial policies under asymmetric information

2007

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We propose an extension of the standard general equilibrium model with production and incomplete markets to situations in which (i) private investors have limited information on the returns of specific assets, (ii) managers of firms have limited information on the preferences of individual shareholders. The extension is obtained by the assumption that firms are not traded directly but grouped into 'sectorial' funds. In our model the financial policy of the firm is not irrelevant; we define a decision criterion for the firm that takes into account both its production and financial decisions. With this criterion, we prove the existence of equilibria. Then we discuss the nature of the inefficiencies introduced by the presence asymmetric information. In an appendix we illustrate the properties of the model in the CAPM framework. Abstract. We propose an extension of the standard general equilibrium model with production and incomplete markets to situations in which (i) private investors have limited information on the returns of specific assets, (ii) managers of firms have limited information on the preferences of individual shareholders. The extension is obtained by the assumption that firms are not traded directly but grouped into 'sectorial' funds. In our model the financial policy of the firm is not irrelevant; we define a decision criterion for the firm that takes into account both its production and financial decisions. With this criterion, we prove the existence of equilibria. Then we discuss the nature of the inefficiencies introduced by the presence asymmetric information. In an appendix we illustrate the properties of the model in the CAPM framework.

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Chapter 30 Incomplete markets

Cited by 77 publications

References 57 publications

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

On the existence of approximated equilibria in discontinuous economies

Production and financial policies under asymmetric information

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