On the Different Notions of Arbitrage and Existence of Equilibrium

Dana, Rose‐Anne; Van, Cuong Le; Magnien, François

doi:10.1006/jeth.1999.2518

Cited by 49 publications

(52 citation statements)

References 22 publications

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“…Our argument is based on the fact that for an agent which is sensitive to large losses, it is sufficient to search for optimal one-time-step strategies in conditionally compact sets. For different conditions and concepts of compactness in equilibrium models with consumption sets that are unbounded from below, we refer to Werner (1987), Cheng (1991), Brown and Werner (1995), Dana et al (1997Dana et al ( , 1999 and the references therein. Duffie (1987) has shown the existence of an equilibrium in in a model with complete spot markets and an incomplete market of purely financial securities.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

Cheridito

Horst

Kupper³

et al. 2011

SSRN Journal

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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

Cheridito

Horst

Kupper³

et al. 2011

SSRN Journal

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“…We adapt the proof given in Dana, Le Van and Magnien (1999) for an exchange exconomy. A detailed proof is given in Appendix 1.…”

Section: The Resultsmentioning

confidence: 99%

No-arbitrage condition and existence of equilibrium with dividends

Van

Minh²

2007

Journal of Mathematical Economics

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“…Other su cient conditions were given. For a review of the subject in finite dimension, see Allouch et al [1], Dana et al [5], Page [13], [14]. All this trend of literature assumes complete preferences.…”

Section: Introductionmentioning

confidence: 99%

Efficient allocations and equilibria with short-selling and incomplete preferences

Dana

Van

2014

Journal of Mathematical Economics

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This article reconsiders the theory of existence of e cient allocations and equilibria when consumption sets are unbounded below under the assumption that agents have incomplete preferences. It is motivated by an example in the theory of assets with short-selling where there is risk and ambiguity. Agents have Bewley's incomplete preferences. As an inertia principle is assumed in markets, equilibria are individually rational. It is shown that a necessary and su cient condition for the existence of an individually rational e cient allocation or of an equilibrium is that the relative interiors of the risk adjusted sets of probabilities intersect. The more risk averse, the more ambiguity averse the agents, the more likely is an equilibrium to exist. The paper then turns to incomplete preferences represented by a family of concave utility functions. Several definitions of e ciency and of equilibrium with inertia are considered. Su cient conditions and necessary and su cient conditions are given for the existence of e cient allocations and equilibria with inertia.

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On the Different Notions of Arbitrage and Existence of Equilibrium

Cited by 49 publications

References 22 publications

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

No-arbitrage condition and existence of equilibrium with dividends

Efficient allocations and equilibria with short-selling and incomplete preferences

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