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Rational Exuberance
 Journal of Economic Literature
, 2004
"... Consider the postage stamp. As title to a future good (or, in this case, service) with monetary value, this humble object is essentially the same as a security. Its value, 37 cents, can be identiÞed with the present value of the service (delivery of a letter) to which its owner is entitled. ..."
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Cited by 19 (0 self)
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Consider the postage stamp. As title to a future good (or, in this case, service) with monetary value, this humble object is essentially the same as a security. Its value, 37 cents, can be identiÞed with the present value of the service (delivery of a letter) to which its owner is entitled.
Asset Price Bubbles in Complete Markets
"... This paper reviews and extends the mathematical finance literature on bubbles in complete markets. We provide a new characterization theorem for bubbles under the standard no arbitrage (NFLVR) framework, showing that bubbles can be of three types. Type 1 bubbles are uniformly integrable martingale ..."
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Cited by 15 (4 self)
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This paper reviews and extends the mathematical finance literature on bubbles in complete markets. We provide a new characterization theorem for bubbles under the standard no arbitrage (NFLVR) framework, showing that bubbles can be of three types. Type 1 bubbles are uniformly integrable martingales, and these can exist with an infinite lifetime. Type 2 bubbles are nonuniformly integrable martingales, and these can exist for a finite, but unbounded, lifetime. Last, type 3 bubbles are strict local martingales, and these can exist for a finite lifetime only. When one adds a no dominance assumption (from Merton [24]), only type 1 bubbles remain. In addition, under Merton’s no dominance hypothesis, putcall parity holds and there are no bubbles in standard call and put options. Our analysis implies that if one believes asset price bubbles exist and are an important economic phenomena, then asset markets must be incomplete.
Strict local martingales, bubbles, and no early exercise
, 2007
"... We show pathological behavior of asset price processes modeled by continuous strict local martingales under a riskneutral measure. The inspiration comes from recent results on financial bubbles. We analyze, in particular, the effect of the strict nature of the local martingale on the usual formula ..."
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Cited by 5 (0 self)
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We show pathological behavior of asset price processes modeled by continuous strict local martingales under a riskneutral measure. The inspiration comes from recent results on financial bubbles. We analyze, in particular, the effect of the strict nature of the local martingale on the usual formula for the price of a European call option, especially a strong anomaly when call prices decay monotonically with maturity. A complete and detailed analysis for the archetypical strict local martingale, the reciprocal of a three dimensional Bessel process, has been provided. Our main tool is based on a general htransform technique (due to Delbaen and Schachermayer) to generate positive strict local martingales. This gives the basis for a statistical test to verify a suspected bubble is indeed one (or not).
InÞnite Portfolio Strategies
, 2002
"... In inÞnitedate models the received deÞnitions of the payoffs ofÞnite portfolio strategies imply discontinuous valuation. Accordingly, in the absence of trading restrictions, arbitrage results when inÞnite trading strategies are admitted. We propose an alternative that is free of these problems. The ..."
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Cited by 1 (1 self)
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In inÞnitedate models the received deÞnitions of the payoffs ofÞnite portfolio strategies imply discontinuous valuation. Accordingly, in the absence of trading restrictions, arbitrage results when inÞnite trading strategies are admitted. We propose an alternative that is free of these problems. The alternative produces a cleaner, if more abstract, treatment of equilibrium in Þnancial models in inÞnitedate settings. We consider the bearing of the revised treatment on the theory of overlapping generations models and equivalent martingale measures. 1
Werner is a professor of economics at the University of Minnesota. The authors acknowledge helpful
, 2002
"... We show that ArrowDebreu equilibria with countably additive prices in infinitetime economy under uncertainty can be implemented by trading infinitelylived securities in complete sequential markets under two different portfolio feasibility constraints: wealth constraint, and essentially bounded po ..."
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We show that ArrowDebreu equilibria with countably additive prices in infinitetime economy under uncertainty can be implemented by trading infinitelylived securities in complete sequential markets under two different portfolio feasibility constraints: wealth constraint, and essentially bounded portfolios. Sequential equilibria with no price bubbles implement ArrowDebreu equilibria, while those with price bubbles implement ArrowDebreu equilibria with transfers. Transfers are equal to price bubbles on initial portfolio holdings. Price bubbles arise in sequential equilibrium under the wealth constraint if some securities are in zero supply or negative prices are permitted, but cannot arise with essentially bounded portfolios. JEL Classification Codes: D50, G12, E44. Equilibrium models of dynamic competitive economies extending over infinite time play an important role in contemporary economic theory. The basic solution concept for such models is the ArrowDebreu (or Walrasian) equilibrium. In ArrowDebreu equilibrium it is assumed that agents simultaneously trade arbitrary
General Equilibrium, Wariness and Bubbles ∗
"... Faculdade de Economia, Universidade Nova de Lisboa, Portugal. Abstract: We say that a consumer is wary if she overlooks gains but not losses in remote sets of dates or states. We formulate this by requiring preferences to be upper but not lower Mackey semicontinuous and Bewley’s result on existence ..."
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Faculdade de Economia, Universidade Nova de Lisboa, Portugal. Abstract: We say that a consumer is wary if she overlooks gains but not losses in remote sets of dates or states. We formulate this by requiring preferences to be upper but not lower Mackey semicontinuous and Bewley’s result on existence of ArrowDebreu equilibrium whose prices are not necessarily countably additive holds. We relate wariness to some concepts studied in decision theory like lack of myopia and ambiguity aversion. Wary infinite lived agents are not impatient, have optimality conditions, in the form of weaker transversality conditions, that allow them to be creditors at infinity and bubbles occur for positive net supply assets completing the markets. In a two date economy, with infinite states, wary agents are not myopic and bubbles occur, as asset prices do not have to equal the series of returns weighted by state prices. A large class of efficient allocations can only be implemented with asset bubbles. Pessimistic attitudes lead agents to overvalue assets or durable goods with hedging properties, like gold.