Power Utility Maximization in Discrete-Time and Continuous-Time Exponential Levy Models

Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strategies to the continuous-time counterpart. In addition, we provide and compare qualitative properties of the discrete-time and continuous-time optimizers.Comment: 18 pages, to appear in Mathematical Methods of Operations Research. The final publication is available at springerlink.co

Assessing the role of EO in biodiversity monitoring: options for integrating in-situ observations with EO within the context of the EBONE concept

The European Biodiversity Observation Network (EBONE) is a European contribution on terrestrial monitoring to GEO BON, the Group on Earth Observations Biodiversity Observation Network. EBONE’s aims are to develop a system of biodiversity observation at regional, national and European levels by assessing existing approaches in terms of their validity and applicability starting in Europe, then expanding to regions in Africa. The objective of EBONE is to deliver: 1. A sound scientific basis for the production of statistical estimates of stock and change of key indicators; 2. The development of a system for estimating past changes and forecasting and testing policy options and management strategies for threatened ecosystems and species; 3. A proposal for a cost-effective biodiversity monitoring system. There is a consensus that Earth Observation (EO) has a role to play in monitoring biodiversity. With its capacity to observe detailed spatial patterns and variability across large areas at regular intervals, our instinct suggests that EO could deliver the type of spatial and temporal coverage that is beyond reach with in-situ efforts. Furthermore, when considering the emerging networks of in-situ observations, the prospect of enhancing the quality of the information whilst reducing cost through integration is compelling. This report gives a realistic assessment of the role of EO in biodiversity monitoring and the options for integrating in-situ observations with EO within the context of the EBONE concept (cfr. EBONE-ID1.4). The assessment is mainly based on a set of targeted pilot studies. Building on this assessment, the report then presents a series of recommendations on the best options for using EO in an effective, consistent and sustainable biodiversity monitoring scheme. The issues that we faced were many: 1. Integration can be interpreted in different ways. One possible interpretation is: the combined use of independent data sets to deliver a different but improved data set; another is: the use of one data set to complement another dataset. 2. The targeted improvement will vary with stakeholder group: some will seek for more efficiency, others for more reliable estimates (accuracy and/or precision); others for more detail in space and/or time or more of everything. 3. Integration requires a link between the datasets (EO and in-situ). The strength of the link between reflected electromagnetic radiation and the habitats and their biodiversity observed in-situ is function of many variables, for example: the spatial scale of the observations; timing of the observations; the adopted nomenclature for classification; the complexity of the landscape in terms of composition, spatial structure and the physical environment; the habitat and land cover types under consideration. 4. The type of the EO data available varies (function of e.g. budget, size and location of region, cloudiness, national and/or international investment in airborne campaigns or space technology) which determines its capability to deliver the required output. EO and in-situ could be combined in different ways, depending on the type of integration we wanted to achieve and the targeted improvement. We aimed for an improvement in accuracy (i.e. the reduction in error of our indicator estimate calculated for an environmental zone). Furthermore, EO would also provide the spatial patterns for correlated in-situ data. EBONE in its initial development, focused on three main indicators covering: (i) the extent and change of habitats of European interest in the context of a general habitat assessment; (ii) abundance and distribution of selected species (birds, butterflies and plants); and (iii) fragmentation of natural and semi-natural areas. For habitat extent, we decided that it did not matter how in-situ was integrated with EO as long as we could demonstrate that acceptable accuracies could be achieved and the precision could consistently be improved. The nomenclature used to map habitats in-situ was the General Habitat Classification. We considered the following options where the EO and in-situ play different roles: using in-situ samples to re-calibrate a habitat map independently derived from EO; improving the accuracy of in-situ sampled habitat statistics, by post-stratification with correlated EO data; and using in-situ samples to train the classification of EO data into habitat types where the EO data delivers full coverage or a larger number of samples. For some of the above cases we also considered the impact that the sampling strategy employed to deliver the samples would have on the accuracy and precision achieved. Restricted access to European wide species data prevented work on the indicator ‘abundance and distribution of species’. With respect to the indicator ‘fragmentation’, we investigated ways of delivering EO derived measures of habitat patterns that are meaningful to sampled in-situ observations

Overvåking av langtransporterte forurensninger 2009. sammendragsrapport

Rapporten presenterer sammendrag av resultatene for 2009 fra tre overvåkingsprogrammer: “Overvåking av langtrans­portert forurenset luft og nedbør”, ”Overvåkingsprogram for skogskader” (OPS) og “Program for terrestrisk naturovervåking” (TOV). The report presents results for 2009 from three national monitoring programmes on long-range transboundary air pollution

The Nature Index: A General Framework for Synthesizing Knowledge on the State of Biodiversity

The magnitude and urgency of the biodiversity crisis is widely recognized within scientific and political organizations. However, a lack of integrated measures for biodiversity has greatly constrained the national and international response to the biodiversity crisis. Thus, integrated biodiversity indexes will greatly facilitate information transfer from science toward other areas of human society. The Nature Index framework samples scientific information on biodiversity from a variety of sources, synthesizes this information, and then transmits it in a simplified form to environmental managers, policymakers, and the public. The Nature Index optimizes information use by incorporating expert judgment, monitoring-based estimates, and model-based estimates. The index relies on a network of scientific experts, each of whom is responsible for one or more biodiversity indicators. The resulting set of indicators is supposed to represent the best available knowledge on the state of biodiversity and ecosystems in any given area. The value of each indicator is scaled relative to a reference state, i.e., a predicted value assessed by each expert for a hypothetical undisturbed or sustainably managed ecosystem. Scaled indicator values can be aggregated or disaggregated over different axes representing spatiotemporal dimensions or thematic groups. A range of scaling models can be applied to allow for different ways of interpreting the reference states, e.g., optimal situations or minimum sustainable levels. Statistical testing for differences in space or time can be implemented using Monte-Carlo simulations. This study presents the Nature Index framework and details its implementation in Norway. The results suggest that the framework is a functional, efficient, and pragmatic approach for gathering and synthesizing scientific knowledge on the state of biodiversity in any marine or terrestrial ecosystem and has general applicability worldwide