Minimizing the Probability of Ruin in Retirement

Retirees who exhaust their savings while still alive are said to experience financial ruin. These savings are typically grown during the accumulation phase then spent during the retirement decumulation phase. Extensive research into invest-and-harvest decumulation strategies has been conducted, but recommendations differ markedly. This has likely been a source of concern and confusion for the retiree. Our goal is to find what has heretofore been elusive, namely an optimal decumulation strategy. Optimality implies that no alternate strategy exists or can be constructed that delivers a lower probability of ruin, given a fixed inflation-adjusted withdrawal rate.Comment: Proofs appendix with full C++ implementation is include

A Mathematical Approach to the Study of the United States Code

The United States Code (Code) is a document containing over 22 million words that represents a large and important source of Federal statutory law. Scholars and policy advocates often discuss the direction and magnitude of changes in various aspects of the Code. However, few have mathematically formalized the notions behind these discussions or directly measured the resulting representations. This paper addresses the current state of the literature in two ways. First, we formalize a representation of the United States Code as the union of a hierarchical network and a citation network over vertices containing the language of the Code. This representation reflects the fact that the Code is a hierarchically organized document containing language and explicit citations between provisions. Second, we use this formalization to measure aspects of the Code as codified in October 2008, November 2009, and March 2010. These measurements allow for a characterization of the actual changes in the Code over time. Our findings indicate that in the recent past, the Code has grown in its amount of structure, interdependence, and language.Comment: 5 pages, 6 figures, 2 tables

Drought risk management in southern Africa. The potential of long lead climate forecasts for improved drought management

Although climate variability is the single most important factor affecting the livelihood of the people of southern Africa, there is no country in which drought risk is managed well. This mission set out to determine whether the social and economic benefits from making use of long lead climate forecast techniques for managing drought risk in southern Africa would justify investment directed towards bringing forward the techniques into operational usage. The four person mission consulted a wide range of decision makers, weather information users and technical specialists in Botswana, Malawi, South Africa and Zimbabwe during the month of July 1995. The views of those consulted were markedly positive and convergent. Reliable drought prediction is a very high priority for the people and economies of southern Africa. The mission found that: while climates are always changing, southern Africa does indeed appear to be becoming increasingly drought affected; for many governments, people and purposes in the region, reliable indication of the quality of the next wet season is probably the most useful single item of information that could be provided; ongoing climate research is much closer than is generally appreciated to being able to provide reliable and timely information of this kind; It is not logical to wait for forecast skill to be 100% reliable before beginning to incorporate forecasts into decision making meteorological institutions in the region are not capable of realising the full potential of their global links in their present state: they need both investment and development; while improved long lead forecasts offer the prospect of significant benefits, these will not be fully realised without a number of concurrent developments across the economy. The mission concludes that relatively modest investment towards both improving climate prediction and strengthening information dissemination and uptake pathways could revolutionise drought risk 'management-enhancing economic responsibility, food security and natural resource management throughout the region. Benefits from the better management of strategic grain reserves alone would justify the necessary investment. The mission recommends that ODA, the World Bank and other development organisations recognise the important potential of these techniques for mitigating many of the effects of recurrent drought, and seek the means to ensure their broad multi-disciplinary implementation for maximum impact and benefit

Hippopotamid dispersal across the Mediterranean in the latest Miocene: A re-evaluation of the Gravitelli record from Sicily, Italy

The first dispersal of Hippopotamidae out of Africa is recorded around 6 Ma, but this event is documented only in a few European localities. Among them, the uppermost Miocene deposits of Gravitelli in Sicily yielded particularly abundant hippopotamid remains. These specimens, published at the beginning of the 20th century, went lost during the 1908 earthquake that destroyed the city of Messina. The specimens from Gravitelli were ascribed to a new species, Hippopotamus siculus; their generic attribution was not questioned during the first half of the past century and they have not been revised in recent decades. The remains of the Gravitelli hippopotamid were mainly represented by isolated teeth and a few postcranial remains. Morphological and dimensional characters of the specimens, such as long lower premolars, lowcrowned molars, a lower canine with longitudinal ridges and a groove on the lateral surface and the overall dimensions suggest that the Sicilian hippopotamid was characterized by plesiomorphic features. The morphology of the specimens collected from Gravitelli is similar to that of Hexaprotodon? crusafonti, Archaeopotamus harvardi, Hexaprotodon sivalensis and Hexaprotodon garyam. Hexaprotodon? siculus is also morphometrically similar to Hexaprotodon sivalensis, but the lower premolars in the former are longer and wider than in the latter. Accordingly, we provisionally refer the Gravitelli hippopotamid to the genus Hexaprotodon. Hexaprotodon? siculus is dimensionally different from the Spanish latest Miocene hippopotamid, herein referred to as Archaeopotamus crusafonti, and the two species are considered as valid taxa. The paleobiogeography of the latest Miocene hippopotamids from the Mediterranean Basin is discussed