Are Retirement Savings Too Exposed to Market Risk?

The stock market, as measured by the broad-based Wilshire 5000, declined by 42 percent between its peak in October 9, 2007 and October 9, 2008. Over that one-year period, the value of equities in pension plans and household portfolios fell by $7.4 trillion. Of that$7.4 trillion decline, $2.0 trillion occurred in 401(k)s and Individual Retirement Accounts (IRAs),$1.9 trillion in public and private defined benefit plans, and $3.6 trillion in household non-pension assets. This brief documents where the declines occurred. This information is interesting and important in its own right. But the declines also highlight the fragility of our emerging pension arrangements. Today the declines were divided equally between defined benefit and defined contribution plans, but in the future individuals will bear the full brunt of market turmoil as the shift to 401(k)s continues. Much of the reform discussion regarding private sector employer-sponsored pensions has focused on extending coverage. But the current financial tsunami also underlines the need to construct arrangements where the full market risk does not fall on pension participants.

Periodically refreshed multiply exposed photorefractive holograms

We describe a method for increasing the diffraction efficiency of multiply exposed photorefractive holograms by periodic copying. The method is experimentally demonstrated with photorefractive and thermoplastic recording media

Exposed faces of semidefinitely representable sets

A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite. Motivated by the fact that diagonal LMIs define polyhedra, the solution set of an LMI is called a spectrahedron. Linear images of spectrahedra are called semidefinite representable sets. Part of the interest in spectrahedra and semidefinite representable sets arises from the fact that one can efficiently optimize linear functions on them by semidefinite programming, like one can do on polyhedra by linear programming. It is known that every face of a spectrahedron is exposed. This is also true in the general context of rigidly convex sets. We study the same question for semidefinite representable sets. Lasserre proposed a moment matrix method to construct semidefinite representations for certain sets. Our main result is that this method can only work if all faces of the considered set are exposed. This necessary condition complements sufficient conditions recently proved by Lasserre, Helton and Nie

Rank properties of exposed positive maps

Let \cK and \cH be finite dimensional Hilbert spaces and let \fP denote the cone of all positive linear maps acting from \fB(\cK) into \fB(\cH). We show that each map of the form $\phi(X)=AXA^*$ or $\phi(X)=AX^TA^*$ is an exposed point of \fP. We also show that if a map $\phi$ is an exposed point of \fP then either $\phi$ is rank 1 non-increasing or \rank\phi(P)>1 for any one-dimensional projection P\in\fB(\cK).Comment: 6 pages, last section removed - it will be a part of another pape

Microcraters in aluminum foils exposed by Stardust

We will present preliminary results on the nature and size frequency distribution of microcraters that formed in aluminum foils during the flyby of comet Wild 2 by the Stardust spacecraft