The implication of the hyperbolic discount model for annuitisation decisions

The low demand for immediate annuities at retirement has been a long-standing puzzle. We show that a hyperbolic discount model can explain this behaviour and results in the attractiveness of long-term deferred annuities. With a set of benchmark assumptions, we find that retirees would be willing to pay a much higher price than the actuarial fair price for annuities with longer deferred periods. Moreover, if governments were to introduce a pre-commitment device which requires pensioners to make annuitisation decisions around ten years before retirement, the take up rate of annuities could become higher

Conserved Linking in Single- and Double-Stranded Polymers

We demonstrate a variant of the Bond Fluctuation lattice Monte Carlo model in which moves through cis conformations are forbidden. Ring polymers in this model have a conserved quantity that amounts to a topological linking number. Increased linking number reduces the radius of gyration mildly. A linking number of order 0.2 per bond leads to an eight-percent reduction of the radius for 128-bond chains. This percentage appears to rise with increasing chain length, contrary to expectation. For ring chains evolving without the conservation of linking number, we demonstrate a substantial anti-correlation between the twist and writhe variables whose sum yields the linking number. We raise the possibility that our observed anti-correlations may have counterparts in the most important practical polymer that conserves linking number, DNA.Comment: Revised title, minor changes, updated references. 36 pages, including 14 figures. More formats available at http://rainbow.uchicago.edu/~plewa/webpaper

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

Illinois River 2001 Pollutant Loads At Arkansas Highway 59 Bridge

Automatic water samplers and a U. S. Geological Survey gauging station were established in 1995 on the main stem of the Illinois River at the Arkansas Highway 59 Bridge. Since that time, continuous stage and discharge measurements and water quality sampling have been used to determine pollutant concentrations and loads in the Arkansas portion of the Illinois River. This report represents the results from the measurement and sampling for January 1, 2001 to December 31, 2001

Illinois River 1998 Nutrient and Suspended Sediment Loads at Arkansas Highway 59 Bridge

Automatic water samplers and a U.S. Geological Survey (USGS) gauging station were established in 1995 on the main stem of the Illinois River at the Arkansas Highway 59 Bridge. Since that time, continuous stage and discharge measurements and water quality sampling have been used to determine pollutant concentrations and loads in the Arkansas portion of the Illinois River. This report represents the results from the measurement and sampling for January 1, 1998 to December 31, 1998