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.

We show pathological behavior of asset price processes modeled by continuous strict local martingales under a risk-neutral 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 h-transform 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).

This paper studies a rational price bubble in a productive asset and its e¤ect on the real economy in an overlapping generations model of a small open economy with an analysis on a collateralized credit constraint. As a consequence, the small open economy is vunerable to the bubble emergence. Crucially for the policy-making, the credit constraint plays a double-bladed role in the bubble emergence. That is, with the natural credit limit which is evaluated at the fundamental value of the collateral, a bubble cannot exist; while, if the …nancial intermediary sets the credit limit at the expected value of the collateral, the credit constraint instead helps support the bubble. Hence, the tight …nancial regulation and supervision over the credit constraint are recommended for policymakers to prevent or terminate the bubble. 1

This research owes an intellectual debt to a few good citizens of Stavropol, Russia, who showed me the many marvels of unbridled capitalism. I am grateful for a USAID grant through the Eurasia Foundation, which made possible the trip to Russia in 1993, and to Duke University for financing the trip in 1994. Klarita Sadiraj helped me understand the Albanian Ponzi schemes, while Oleg Mikhalev provided perspective on the Russian Ponzi schemes. Frank Acito, Sugato Bhattacharyya, Timothy Crack, Craig Holden, Rich Rosen, Richard Shockley, Gregg Udell and seminar participants at Indiana, Maryland and Wisconsin (Madison) provided many thoughtful comments. I am particularly grateful to Mukarram Attari This paper shows that transition economies are breeding grounds for Ponzi schemes. It details how an unscrupulous profit-maximizing promoter can design classical Ponzi schemes if the following conditions are met: a large public sector (the proportion of national wealth owned by the state is above a lower bound), ambiguous laws governing the transfer of property rights from the state to the citizen (victims of a failed Ponzi scheme may organize to use the state’s assets for a bailout, the probability of which occurring is above a lower bound), political connections (the probability of early termination of the Ponzi scheme by a regulator is below an upper bound) and an inexpensive access to citizens through mass-media (advertising

We show that Arrow-Debreu equilibria with countably additive prices in infinite-time economy under uncertainty can be implemented by trading infinitely-lived securities in complete sequential markets under two different portfolio feasibility constraints: wealth constraint, and essentially bounded portfolios. Sequential equilibria with no price bubbles implement Arrow-Debreu equilibria, while those with price bubbles implement Arrow-Debreu 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 Arrow-Debreu (or Walrasian) equilibrium. In Arrow-Debreu equilibrium it is assumed that agents simultaneously trade arbitrary

This paper argues that the introduction of a short-sale constraint in the Arrow-Radner framework invalidates standard definitions of complete and incomplete markets. In this constrained set-up, two threshold values with familiar properties arise. The case of a zero short-sale bound set on some security fulfills the standard definition of “incomplete ” financial markets. Beyond a particular level of the short-sale bound financial markets are “complete”, since the short-sale constraint is not active. For intermediate bounds the distinction between complete and incomplete financial markets is blurred. Although some technical definitions hold, agents can not fully transfer wealth among states. These intermediate cases, called “technically incomplete markets”, exhibit interesting welfare properties. For instance, the resulting equilibrium allocations may not be Pareto dominated by those of the non-restricted complete markets equilibrium.

Analysis of continuous strict local martingales via h-transforms

We provide an in…nite-horizon model of a production economy with bubbles, in which …rms meet stochastic investment opportunities and face credit constraints. Capital is not only an input for production, but also serves as collateral. We show that bubbles on this reproducible asset may arise, which relax collateral constraints and improve investment e ¢ ciency. The collapse of bubbles leads to a recession. We show that there is a credit policy that can eliminate the bubble on …rm assets and can achieve the e ¢ cient allocation.

We provide an in…nite-horizon model of a production economy with credit-driven stockprice bubbles, in which …rms meet stochastic investment opportunities and face credit constraints. Capital is not only an input for production, but also serves as collateral. We show that bubbles on this reproducible asset may arise, which relax collateral constraints and improve investment e ¢ ciency. The collapse of bubbles leads to a recession and a stock market crash. We show that there is a credit policy that can eliminate the bubble on …rm