Efficient and proper Generalised Linear Models with power link functions

The generalised linear model is a flexible predictive model for observational data that is widely used in practice as it extends linear regression models to non-Gaussian data. In this paper we introduce the concept of a properly defined generalised linear model by requiring the conditional mean of the response variable to be properly mapped through the chosen link function and the log-likelihood function to be concave. We provide a comprehensive classification of proper generalised linear models for the Tweedie family and its popular subclasses under different link function specifications. Our main theoretical findings show that most Tweedie generalised linear models are not proper for canonical and log link functions, and identify a rich class of proper Tweedie generalised linear models with power link functions. Using self-concordant log-likelihoods and linearisation techniques, we provide novel algorithms for estimating several special cases of proper and not proper Tweedie generalised linear models with power link functions. The effectivenes of our methods is determined through an extensive numerical comparison of our estimates and those obtained using three built-in packages, MATLAB f itglm, R glm2 and Python sm.GLM libraries, which are all implemented based on the standard Iteratively Reweighted Least Squares method. Overall, we find that our algorithms consistently outperform these benchmarks in terms of both accuracy and efficiency, the largest improvements being documented for high-dimensional settings

Mars climate engineering using orbiting solar reflectors

The manned mission is seen as a first step towards a Mars surface exploration base-station and, later, establishing permanent settlement. The location and use of Mars's natural resources is vital to enable cost-effective long-duration human exploration and exploitation missions as well as subsequent human colonization. Planet resources include various crust-lodged materials, a low-pressure natural atmosphere, assorted forms of utilizable energy, lower gravity than Earth's, and ground placement advantages relative to human operability and living standards. Power resources may include using solar and wind energy, importation of nuclear reactors and the harvesting of geothermal potential. In fact, a new branch of human civilization could be established permanently on Mars in the next century. But, meantime, an inventory and proper social assessment of Mars's prospective energy and material resources is required. This book investigates the possibilities and limitations of various systems supplying manned bases on Mars with energy and other vital resources. The book collects together recent proposals and innovative options and solutions. It is a useful source of condensed information for specialists involved in current and impending Mars-related activities and a good starting point for young researchers

The Hormuz Strait Dam Macroproject— 21st Century Electricity Development Infrastructure Node (EDIN)?

Ocean gulfs offer a means of artificially creating a depression, which can be used for a regionally significant hydroelectric macroproject. We examine here the case for a dam at the Strait of Hormuz that blocks a large gulf situated in an arid region. A 35 m evaporation of this concentration basin will reduce its watery surface area by ~53% and allow generation of ~2.050 MW (or possibly ~ 2.500 MW) of electricity. Our conclusion is that the proposed Electricity Development Infrastructure Node (EDIN) is a feasible and desirable macroproject. If the macroproject starts in the near-term future, it would require a significant change in the logistics of oil and gas transport from this region. Alternatively, it can be considered as an attractive future solution for the energy requirements of the region after the exhaustion of its oil and gas reserves

Photon assisted Levy flights of minority carriers in n-InP

We study the photoluminescence spectra of n-doped InP bulk wafers, both in the reflection and the transmission geometries relative to the excitation beam. From the observed spectra we estimate the spatial distribution of minority carriers allowing for the spectral filtering due to re-absorption of luminescence in the wafer. This distribution unambiguously demonstrates a non-exponential drop-off with distance from the excitation region. Such a behavior evidences an anomalous photon-assisted transport of minority carriers enhanced owing to the high quantum efficiency of emission. It is shown that the transport conforms very well to the so-called Levy-flights process corresponding to a peculiar random walk that does not reduce to diffusion. The index gamma of the Levy flights distribution is found to be in the range gamma = 0.64 to 0.79, depending on the doping. Thus, we propose the high-efficiency direct-gap semiconductors as a remarkable laboratory system for studying the anomalous transport.Comment: 12 pages, 9 figure

Extremes on the discounted aggregate claims in a time dependent risk model

This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables (rv's). Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed rv's. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims. A simulation study is performed in order to validate the results obtained in the free interest risk model

Delayed Capital Injections for a Risk Process with Markovian Arrivals

In this paper we propose a generalisation to the Markov Arrival Process (MAP) risk model, by allowing for a delayed receipt of required capital injections whenever the surplus of an insurance firm is negative. Delayed capital injections often appear in practice due to the time taken for administrative and processing purposes of the funds from a third party or the shareholders of a firm. We introduce a MAP risk model that allows for capital injections to be received instantaneously, or with a random delay, depending on the amount of deficit experienced by the firm. For this model, we derive a system of Fredholm integral equations of the second kind for the Gerber-Shiu function and obtain an explicit expression (in matrix form) in terms of the Gerber-Shiu function of the MAP risk model without capital injections. In addition, we show that the expected discounted accumulated capital injections and the expected discounted overall time in red, up to the time of ruin, satisfy a similar integral equation, which can also be solved explicitly. Finally, to illustrate the applicability of our results, numerical examples are given

Efficient risk allocation within a non-life insurance group under Solvency II Regime

Intra-group transfers are risk management tools that are usually widely used to optimise the risk position of an insurance group. In this paper, it is shown that premium and liability transfers could be optimally made in such a way as to reduce the amount of Technical Provisions and Minimum Capital Requirement for the entire insurance conglomerate. These levels of required capital represent the minimal amount that needs to be held by the insurance group without regulator intervention, according to the Solvency II regulation. We assume that only proportional risk transfers are feasible, since such transfers are not difficult to administer for a large scaled insurance group, as is always the case. In addition, any risk shifting should be made for commercial purposes in order to be considered acceptable by the local regulators that impose restrictions on how much the assets within an insurance group are fungible. Our numerical examples illustrate the efficiency of the optimal proportional risk transfers which can easily be implemented, in terms of computation, in any well-known solver even for an insurance conglomerate with many subsidiaries. We found that our proposed optimal proportional allocations are more beneficial for large insurance group, since the relative reduction in capital requirement tends to be small, whereas the gain in absolute terms is quite significant for large scaled insurance group