Optimal consumption and investment with bounded downside risk for power utility functions

We investigate optimal consumption and investment problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall. We formulate various utility maximization problems, which can be solved explicitly. We compare the optimal solutions in form of optimal value, optimal control and optimal wealth to analogous problems under additional uniform risk bounds. Our proofs are partly based on solutions to Hamilton-Jacobi-Bellman equations, and we prove a corresponding verification theorem. This work was supported by the European Science Foundation through the AMaMeF programme.Comment: 36 page

Combination of Persistent Scatterer Interferometry and Single-Baseline Polarimetric Coherence Optimisation to Estimate Deformation Rates with Application to Tehran Basin

This study reports on the monitoring of land subsidence in a rural area located in the southwest of the Tehran basin, Iran, by combining a persistent scatterer interferometry (PSI) method with a single-baseline polarimetric coherence optimisation. Owing to vegetation coverage in this rural area, coherence level experiences a decline and the performance and coverage of conventional interferometry to estimate deformation rate reduces concomitantly. Since the launch of satellites with polarimetric information, the polarimetric InSAR (PolInSAR) technique, which is vector interferometry with different polarimetric channels, has been introduced to optimise the coherence level. One of the most common criteria to select PS pixels is coherence and maximising the coherence can lead to an increased number of selected PS pixels and enhanced PSI performance. The single-baseline polarimetric coherence optimisation method assumes equal polarisation states at the end of each baseline. In order to apply this technique in our study, two different multi-look windows for coherence calculation and also two TerraSAR-X data sets with different numbers of images are used to assess their effect on the polarimetric PSI. Combination of the single-baseline coherence optimisation method with PSI shows significant improvements (more than 50%) in terms of the number of selected PS pixels in the case study even using a data set with a small number of images. A 15 × 15 multi-look window selects a greater number of PS pixels compared to a 9×9 multi-look window, although this entails reducing spatial resolution. The most effective PSI approach in terms of the density of the selected PS turned out to be polarimetric PSI using a data set with a large number of images and a selection of a 15 × 15 multi-look window. Validation of the PSI methods using a large number of images with 9×9 and 15 × 15 multi-look windows via levelling measurements confirms the accuracy and reliability of the results obtained

A Range of Earth Observation Techniques for Assessing Plant Diversity

AbstractVegetation diversity and health is multidimensional and only partially understood due to its complexity. So far there is no single monitoring approach that can sufficiently assess and predict vegetation health and resilience. To gain a better understanding of the different remote sensing (RS) approaches that are available, this chapter reviews the range of Earth observation (EO) platforms, sensors, and techniques for assessing vegetation diversity. Platforms include close-range EO platforms, spectral laboratories, plant phenomics facilities, ecotrons, wireless sensor networks (WSNs), towers, air- and spaceborne EO platforms, and unmanned aerial systems (UAS). Sensors include spectrometers, optical imaging systems, Light Detection and Ranging (LiDAR), and radar. Applications and approaches to vegetation diversity modeling and mapping with air- and spaceborne EO data are also presented. The chapter concludes with recommendations for the future direction of monitoring vegetation diversity using RS