Conditioning super-Brownian motion on its boundary statistics, and fragmentation

We condition super-Brownian motion on "boundary statistics" of the exit measure $X_D$ from a bounded domain $D$. These are random variables defined on an auxiliary probability space generated by sampling from the exit measure $X_D$. Two particular examples are: conditioning on a Poisson random measure with intensity $\beta X_D$ and conditioning on $X_D$ itself. We find the conditional laws as $h$-transforms of the original SBM law using Dynkin's formulation of $X$-harmonic functions. We give explicit expression for the (extended) $X$-harmonic functions considered. We also obtain explicit constructions of these conditional laws in terms of branching particle systems. For example, we give a fragmentation system description of the law of SBM conditioned on $X_D=\nu$, in terms of a particle system, called the backbone. Each particle in the backbone is labeled by a measure $\tilde{\nu}$, representing its descendants' total contribution to the exit measure. The particle's spatial motion is an $h$-transform of Brownian motion, where $h$ depends on $\tilde{\nu}$. At the particle's death two new particles are born, and $\tilde{\nu}$ is passed to the newborns by fragmentation.Comment: Published in at http://dx.doi.org/10.1214/12-AOP778 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Chrysler effect : the impact of the Chrysler bailout on borrowing costs

Did the U.S. government's intervention in the Chrysler reorganization overturn bankruptcy law? Critics argue that the government-sponsored reorganization impermissibly elevated claims of the auto union over those of Chrysler's other creditors. If the critics are correct, businesses might suffer an increase in their cost of debt because creditors will perceive a new risk, that organized labor might leap-frog them in bankruptcy. This paper examines the financial market wherethis effect would be most detectible, the market for bonds of highly unionized companies. The authors find no evidence of a negative reaction to the Chrysler bailout by bondholders of unionized firms. They thus reject the notion that investors perceived a distortion of bankruptcy priorities. To the contrary, bondholders of unionized firms reacted positively to the Chrysler bailout. This evidence suggests that bondholders interpreted the Chrysler bailout as a signal that the government will stand behind unionized firms. The results are consistent with the notion that too-big-to-fail government policies generate moral hazard in the credit markets.Debt Markets,Bankruptcy and Resolution of Financial Distress,Emerging Markets,Deposit Insurance,Access to Finance