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14
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 40 (6 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.
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 36 (2 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.
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 7 (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).
Dividend Policy and Income Taxation
, 2008
"... The e¤ects of dividend and capital gains taxes on optimal dividend payout policy are analyzed in the context of a onegood model (so that capital consists of stored units of the consumption good). The aftertax discount factor is assumed to adjust to taxes to bring about equality between the discoun ..."
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The e¤ects of dividend and capital gains taxes on optimal dividend payout policy are analyzed in the context of a onegood model (so that capital consists of stored units of the consumption good). The aftertax discount factor is assumed to adjust to taxes to bring about equality between the discounted value of the
rms aftertax dividend stream under the optimal dividend policy and the number of units of capital the
rm is operating. A standard result that the MillerModigliani dividend irrelevance proposition applies in the presence of taxes if the dividend tax rate equals the capital gains tax rate (and if capital gains are taxed as they accrue) is demonstrated. The analysis is extended to deal with unequal tax rates. The two major results are (1) allocating retained earnings to share repurchases has the same tax implications as allocating retained earnings to new investments, and (2) either of these will be optimal if and only if the tax rate on capital gains is lower than that on dividends. JEL codes G1, G3. The MillerModigliani [14] dividendirrelevance principle asserts (among other propositions) that, in the absence of frictions, corporate dividend policy does not affect rm value. This is so because if investment is held constant, as MillerModigliani assumed, then by an identity a change in dividends is o¤set oneforone by a change in proceeds from new security issues. Assuming that investors value
rms by discounting payments to stockholders net of proceeds of new issues,
rm value is una¤ected by the dividends change. A related dividendirrelevance proposition, often incorrectly attributed to MillerModigliani, may apply if investment is not held constant: variations in future dividends do not a¤ect
rm value provided that retained earnings are invested in zeronetpresentvalue projects. This invariance is held to occur because the direct e¤ect on rm value of an increase in current dividends increase is exactly o¤set by lower
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
Documents de Travail du Centre d’Economie de la Sorbonne
, 2014
"... On existence and bubbles of Ramsey equilibrium with borrowing constraints ..."
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On existence and bubbles of Ramsey equilibrium with borrowing constraints
unknown title
, 2008
"... Analysis of continuous strict local martingales via htransforms ..."
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Bubbles and the Intertemporal Government Budget Constraint
, 2004
"... Recent years have seen a protracted debate on the "Þscal theory of the price level". This doctrine is based on the intertemporal government budget constraint, which says that the real value of the government debt equals the discounted value of future government surpluses. It is observed t ..."
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Recent years have seen a protracted debate on the "Þscal theory of the price level". This doctrine is based on the intertemporal government budget constraint, which says that the real value of the government debt equals the discounted value of future government surpluses. It is observed that the intertemporal government budget constraint consists of the proposition that government debt management deÞnes a portfolio strategy that has no bubble. Therefore the intertemporal government budget constraint is satisÞed in models in which bubbles can be ruled out, and it fails in settings in which bubbles can occur in equilibrium.
In nite Portfolio Strategies
, 2008
"... Finance models with a
nite number of states and dates have properties that may or may not extend to their in
nite counterparts, depending on how the extension is implemented. It is proposed to deal with this situation by appending a date or state called 1 to the payo ¤ index set, and de
ning a topo ..."
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Finance models with a
nite number of states and dates have properties that may or may not extend to their in
nite counterparts, depending on how the extension is implemented. It is proposed to deal with this situation by appending a date or state called 1 to the payo ¤ index set, and de
ning a topology such that the payo ¤ index set is compact. This allows a simpli
ed mathematical treatment of a number of topics that are unwieldy when modeled in a setting where the payo ¤ index set is noncompact. Applications discussed include the doubling strategy, Ponzi schemes and payo ¤ bubbles. The doubling strategy the portfolio strategy under which the investor doubles the investment in a risky asset until he generates a gain is discussed in practically every introductory graduatelevel text in
nancial economics. The point of most discussions is to provide a purported demonstration that if portfolio strategies in in nitetime settings are unrestricted, arbitrages can be generated. In other words, a portfolio strategy that is increasingly risky in
nite time, and therefore increasingly unattractive to riskaverse investors, morphs into a riskless arbitrage in in
nite time. Such arbitrages, it is held, must be ruled out by restrictions on admissible portfolio strategies. To their credit, some analysts appear to be uneasy about labeling the doubling strategy an arbitrage, particularly in the absence of any characterization of preferences. Delbaen and Schachermayer [3] concluded from the fact that losses are unbounded that [e]verybody, especially a casino boss, knows that [the doubling strategy] is a very risky way of winning 1e. This type of strategy has to be ruled out: there should be a lower bound on the players loss([3] p. 130). This passage is interesting on several levels. Most obviously, under the received treatment the doubling strategy in fact has no risk as we will see, under the usual treatment there exists no I am indebted participants at seminars at the University of California, Santa Barbara, statis