Silent MST approximation for tiny memory

In network distributed computing, minimum spanning tree (MST) is one of the key problems, and silent self-stabilization one of the most demanding fault-tolerance properties. For this problem and this model, a polynomial-time algorithm with $O(\log^2\!n)$ memory is known for the state model. This is memory optimal for weights in the classic $[1,\text{poly}(n)]$ range (where $n$ is the size of the network). In this paper, we go below this $O(\log^2\!n)$ memory, using approximation and parametrized complexity. More specifically, our contributions are two-fold. We introduce a second parameter~$s$, which is the space needed to encode a weight, and we design a silent polynomial-time self-stabilizing algorithm, with space $O(\log n \cdot s)$. In turn, this allows us to get an approximation algorithm for the problem, with a trade-off between the approximation ratio of the solution and the space used. For polynomial weights, this trade-off goes smoothly from memory $O(\log n)$ for an $n$-approximation, to memory $O(\log^2\!n)$ for exact solutions, with for example memory $O(\log n\log\log n)$ for a 2-approximation

Money-back guarantees in individual pension accounts : evidence from the German pension reform

The German Retirement Saving Act instituted a new funded system of supplementary pensions coupled with a general reduction in the level of state pay-as-you-go old-age pensions. In order to qualify for tax relief, the providers of supplementary savings products must offer a guarantee of the nominal value at retirement of contributions paid into these saving accounts. This paper explores how this "money-back" guarantee works and evaluates alternative designs for guarantee structures, including a life cycle model (dynamic asset allocation), a plan with a pre-specified blend of equity and bond investments (static asset allocation), and some type of portfolio insurance. We use a simulation methodology to compare hedging effectiveness and hedging costs associated with the provision of the money-back guarantee. In addition, the guarantee has important implications for regulators who must find an appropriate solvency system for such saving schemes. This version June 17, 2002 . Klassifikation: G11, G23, G2