Arbitrage and the Existence of Competitive Equilibrium

Werner, Jan

doi:10.2307/1913563

Cited by 132 publications

(136 citation statements)

References 4 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

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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“…16 Milne (1995). 17 Werner (1987) and Milne (1995) describe a complete set of assumptions regarding consumer preferences and the convexity and closedness of each consumer's consumption set and a proof of the existence of an equilibrium price vector for current and future claims on consumption in the absence of a bounded consumption set, for an exchange economy with a finite set of states and an asset span of arbitrary dimension. 18 We do not necessarily assume that all agents are risk neutral, needing only the result that assets can be priced as if agents are risk neutral after an appropriate change of measure, reflected in the distribution given in Table 3.…”

Section: The Modelmentioning

confidence: 99%

Insurers are not Banks: Assessing Liquidity, Efficiency and Solvency Risk Under Alternative Approaches to Capital Adequacy

Kupiec

Nickerson

2005

Geneva Pap Risk Insur Issues Pract

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Differences in the portfolios of depositories and insurance and reinsurance firms are important for the design of efficient capital regulations. Using a simple contingent claims model which focuses on credit risk and in which intermediaries issue liabilities under conditions of moral hazard, we illustrate three effects of risk-based capital regulations on institutional solvency risk, liquidity and economic efficiency. First, assuming identical asset risks to depositories, insurers that issue significant amounts of contingent liabilities may exhibit a zero risk of insolvency while holding significantly less equity capital than depositories. Second, higher capital requirements must be placed on depositories to attain the same degree of solvency risk, owing to the riskless payoffs promised for bank deposits and similar liabilities. Third, while bank-based capital regulations cannot resolve losses associated with systemic financial risk, capital regulations that incorporate incentive-compatible tax penalties to mitigate moral hazard effects can do so by increasing both liquidity and spanning. We conclude that distortions occur when measuring the solvency risk of insurers and other non-bank intermediaries with bank-based capital regulations and that uniform harmonization of capital regulations across depositories and insurers can significantly reduce aggregate liquidity and efficiency.

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“…These conditions have been generalized to abstract economies and are known as the existence of no-arbitrage prices condition (see Werner [17]) and the no unbounded utility arbitrage condition (NUBA) ( see Page [14]). They were shown to be equivalent under adequate hypotheses.…”

Section: Introductionmentioning

confidence: 99%

“…As Page [14] and Werner [17], the paper is motivated by an example in the theory of assets with short-selling. Agents are assumed not to have enough information to quantify uncertainty by a single probability, hence each agent has a set of priors.…”

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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Arbitrage and the Existence of Competitive Equilibrium

Cited by 132 publications

References 4 publications

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

Insurers are not Banks: Assessing Liquidity, Efficiency and Solvency Risk Under Alternative Approaches to Capital Adequacy

Efficient allocations and equilibria with short-selling and incomplete preferences

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