Upper and Lower Bounds for Ruin Probability

In this note we discuss upper and lower bound for the ruin probability in an insurance model with very heavy-tailed claims and interarrival times.

An Estimate of the Probability Pr(X

2000 Mathematics Subject Classification: 33C90, 62E99

Time to Extinction in Branching Processes and its Application in Epidemiology

2010 Mathematics Subject Classification: Primary 60J80; Secondary 92D30.

On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density

2000 Mathematics Subject Classification: 62G07, 62L20.

Néhány megjegyzés a kockázat, bizonytalanság, valószínűség kérdéséhez (Some remarks about uncertainty, risk and probability)

A címben említett három fogalom a közgazdasági elméletben központi szerepet foglal el. Ezek viszonya elsősorban a közgazdaságtudományi megismerés határait feszegeti. Mit tudunk a gazdasági döntésekről? Milyen információk alapján születnek a döntések? Lehet-e a gazdasági döntéseket „tudományos” alapra helyezni? A bizonytalanság kérdéséről az 1920-as években való megjelenése óta mindent elmondtak. Megvizsgálták a kérdést filozófiailag, matematikailag. Tárgyalták a kérdés számtalan elméleti és gyakorlati aspektusát. Akkor miért kell sokadszorra is foglalkozni a témával? A válasz igen egyszerű: azért, mert a kérdés minden szempontból ténylegesen alapvető, és mindenkor releváns. Úgy hírlik, hogy a római diadalmenetekben a győztes szekerén mindig volt egy rabszolga is, aki folyamatosan figyelmeztette a diadaltól megmámorosodott vezért, hogy ő is csak egy ember, ezt ne feledje el. A gazdasági döntéshozókat hasonló módon újra és újra figyelmeztetni kell arra, hogy a gazdasági döntések a bizonytalanság jegyében születnek. A gazdasági folyamatok megérthetőségének és kontrollálhatóságának van egy igen szoros korlátja. Ezt a korlátot a folyamatok inherens bizonytalansága adja. A gazdasági döntéshozók fülébe folyamatosan duruzsolni kell: ők is csak emberek, és ezért ismereteik igen korlátozottak. A „bátor” döntések során az eredmény bizonytalan, a tévedés azonban bizonyosra vehető. / === / In the article the author presents some remarks on the application of probability theory in financial decision making. From mathematical point of view the risk neutral measures used in finance are some version of separating hyperplanes used in optimization theory and in general equilibrium theory. Therefore they are just formally a probabilities. They interpretation as probabilities are misleading analogies leading to wrong decisions.

Valószínűség, esély, relatív súlyok. Opciók és reálopciók (Probability, chance, relative weights)

There is a long debate (going back to Keynes) how to interpret the concept of probability in economics, in business decisions, in finance. Iván Bélyácz suggested that the Black–Scholes– Merton analysis of fi nancial derivatives has a contribution to this risk vs. uncertainty debate. This article tries to interpret this suggestion, from the viewpoint of traded options, real options, Arrow–Debreu model, Heath–Jarrow–Morton model, insurance business. The article suggests making clear distinction and using different naming ● when the frequents approach and the statistics is relevant, ● when we just use consequent relative weights during the no-arbitrage pricing, and these weight are just interpreted as probabilities, ● when we just lack the necessary information, and there is a basic uncertainty in the business decision making process. The paper suggests making a sharp distinction between fi nancial derivatives used for market risk management and credit risk type derivatives (CDO, CDS, etc) in the reregulation process of the fi nancial markets.

Identification, distribution, and probability of infection in sympatric gastropods by digenean parasites at Pa-hay-okee, Everglades National Park using molecules and morphology

In this study, I determined the identity, taxonomic placement, and distribution of digenetic trematodes parasitizing the snails Pomacea paludosa and Planorbella duryi at Pa-hay-okee, Everglades National Park. I also characterized temporal and geographic variation in the probability of parasite infection for these snails based on two years of sampling. Although studies indicate that digenean parasites may have important effects both on individual species and the structure of communities, there have been no studies of digenean parasitism on snails within the Everglades ecosystem. For example, the endangered Everglade Snail Kite, a specialist that feeds almost exclusively on Pomacea paludosa, and is known to be a definitive host of digenean parasites, may suffer direct and indirect effects from consumption of parasitized apple snails. Therefore, information on the diversity and abundance of parasites harbored in snail populations in the Everglades should be of considerable interest for management and conservation of wildlife. Juvenile digeneans (cercariae) representing 20 species were isolated from these two snails, representing a quadrupling of the number of species known. Species were characterized based on morphological, morphometric, and sequence data (18S rDNA, COI, and ITS). Species richness of shed cercariae from P. duryi was greater than P. paludosa, with 13 and 7 species respectively. These species represented 14 families. P. paludosa and P. duryi had no digenean species in common. Probability of digenean infection was higher for P. duryi than P. paludosa and adults showed a greater risk of infection than juveniles for both of these snails. Planorbella duryi showed variation in probability of infection between sampling sites and hydrological seasons. The number of unique combinations of multi-species infections was greatest among P. duryi individuals, while the overall percentage of multi-species infections was greatest in P. paludosa. Analyses of six frequently-observed multiple infections from P. duryi suggest the presence of negative interactions, positive interactions, and neutral associations between larval digeneans. These results should contribute to an understanding of the factors controlling the abundance and distribution of key species in the Everglades ecosystem and may in particular help in the management and recovery planning for the Everglade Snail Kite.

Diagnóstico da comercialização de produtos da medicina popular em feiras livres do semiárido do Rio Grande do Norte: avaliações socioeconômicas e sanitárias, com proposta de legislação específica

Historically, man has empirically acquired knowledge about the therapeutic applications of extracted elements of the natural environment in which belonged. Such knowledge over time culminated in the formation of traditional health systems. Among its features, the use of bioactive plant species - medicinal plants - stands out for its efficiency and high popular acceptance. Despite its importance for public health, the population still has in the open-air fairs the main source for the acquisition of the species used. In these spaces, the trade generally occurs informally, under unfavorable conditions to the quality of the products and to the financial sustainability of the business. In this context, this study aimed to characterize the socioeconomic, cultural and sanitary aspects related to the trade of medicinal plants in municipalities of a semiarid region of Rio Grande do Norte, and additionally, proposing a specific legislation to the activity. Socioeconomic data were collected through on-site interviews, guided by structured form. The observations about the hygienic and sanitary adequacy of physical facilities and practices employed at the point of sale /environment were conducted and recorded with the use of assessment tool developed for use in open markets. The adequacy of medicinal plants to consumption was determined by microbiological analysis. The activity was carried out by individuals who are aged between 21 and 81 years of age, low educational level and low-income, predominantly males. The data showed a tendency to extinction of the activity in all the districts studied. It was observed in all the fairs studied hygiene and sanitation inadequacies that characterized very high health risk, representing in this way, the high probability of Food Transmitted Diseases outbreaks Such conditions were reflected in the high percentage of inadequacy to the consumption of the analyzed medicinal plants samples, illustrating the potential health risk to consumers. To contribute to the correction of hygiene and sanitation inadequacies observed in the studied open-air fairs, educational interventions were made to the training of traders in Good Practices. As a complement, was drafted a specific legislation for the marketing of folk medicine's products in open-air fairs. Such actions, products and its developments will contribute significantly to improving the quality of products available to the population and the preservation of activity, potentially reducing the risks to public health.

The star formation and extinction coevolution of UV-selected galaxies over 0.05 < z < 1.2

We use a new stacking technique to obtain mean mid-IR and far-IR to far-UV flux ratios over the rest-frame near-UV, near-IR color-magnitude diagram. We employ COMBO-17 redshifts and COMBO-17 optical, GALEX far- and near-UV, and Spitzer IRAC and MIPS mid-IR photometry. This technique permits us to probe the infrared excess (IRX), the ratio of far-IR to far-UV luminosity, and the specific star formation rate (SSFR) and their coevolution over 2 orders of magnitude of stellar mass and over redshift 0.1 < z < 1.2. We find that the SSFR and the characteristic mass (Script M_0) above which the SSFR drops increase with redshift (downsizing). At any given epoch, the IRX is an increasing function of mass up to Script M_0. Above this mass the IRX falls, suggesting gas exhaustion. In a given mass bin below Script M_0, the IRX increases with time in a fashion consistent with enrichment. We interpret these trends using a simple model with a Schmidt-Kennicutt law and extinction that tracks gas density and enrichment. We find that the average IRX and SSFR follow a galaxy age parameter ξ, which is determined mainly by the galaxy mass and time since formation. We conclude that blue-sequence galaxies have properties which show simple, systematic trends with mass and time such as the steady buildup of heavy elements in the interstellar media of evolving galaxies and the exhaustion of gas in galaxies that are evolving off the blue sequence. The IRX represents a tool for selecting galaxies at various stages of evolution.

Stochastic descriptors to study the fate and potential of naive T cell clonotypes in the periphery

The population of naive T cells in the periphery is best described by determining both its T cell receptor diversity, or number of clonotypes, and the sizes of its clonal subsets. In this paper, we make use of a previously introduced mathematical model of naive T cell homeostasis, to study the fate and potential of naive T cell clonotypes in the periphery. This is achieved by the introduction of several new stochastic descriptors for a given naive T cell clonotype, such as its maximum clonal size, the time to reach this maximum, the number of proliferation events required to reach this maximum, the rate of contraction of the clonotype during its way to extinction, as well as the time to a given number of proliferation events. Our results show that two fates can be identified for the dynamics of the clonotype: extinction in the short-term if the clonotype experiences too hostile a peripheral environment, or establishment in the periphery in the long-term. In this second case the probability mass function for the maximum clonal size is bimodal, with one mode near one and the other mode far away from it. Our model also indicates that the fate of a recent thymic emigrant (RTE) during its journey in the periphery has a clear stochastic component, where the probability of extinction cannot be neglected, even in a friendly but competitive environment. On the other hand, a greater deterministic behaviour can be expected in the potential size of the clonotype seeded by the RTE in the long-term, once it escapes extinction.

Using Bird Distributions to Assess Extinction Risk and Identify Conservation Priorities in Biodiversity Hotspots

Habitat loss, fragmentation, and degradation threaten the World’s ecosystems and species. These, and other threats, will likely be exacerbated by climate change. Due to a limited budget for conservation, we are forced to prioritize a few areas over others. These places are selected based on their uniqueness and vulnerability. One of the most famous examples is the biodiversity hotspots: areas where large quantities of endemic species meet alarming rates of habitat loss. Most of these places are in the tropics, where species have smaller ranges, diversity is higher, and ecosystems are most threatened.

Species distributions are useful to understand ecological theory and evaluate extinction risk. Small-ranged species, or those endemic to one place, are more vulnerable to extinction than widely distributed species. However, current range maps often overestimate the distribution of species, including areas that are not within the suitable elevation or habitat for a species. Consequently, assessment of extinction risk using these maps could underestimate vulnerability.

In order to be effective in our quest to conserve the World’s most important places we must: 1) Translate global and national priorities into practical local actions, 2) Find synergies between biodiversity conservation and human welfare, 3) Evaluate the different dimensions of threats, in order to design effective conservation measures and prepare for future threats, and 4) Improve the methods used to evaluate species’ extinction risk and prioritize areas for conservation. The purpose of this dissertation is to address these points in Colombia and other global biodiversity hotspots.

In Chapter 2, I identified the global, strategic conservation priorities and then downscaled to practical local actions within the selected priorities in Colombia. I used existing range maps of 171 bird species to identify priority conservation areas that would protect the greatest number of species at risk in Colombia (endemic and small-ranged species). The Western Andes had the highest concentrations of such species—100 in total—but the lowest densities of national parks. I then adjusted the priorities for this region by refining these species ranges by selecting only areas of suitable elevation and remaining habitat. The estimated ranges of these species shrank by 18–100% after accounting for habitat and suitable elevation. Setting conservation priorities on the basis of currently available range maps excluded priority areas in the Western Andes and, by extension, likely elsewhere and for other taxa. By incorporating detailed maps of remaining natural habitats, I made practical recommendations for conservation actions. One recommendation was to restore forest connections to a patch of cloud forest about to become isolated from the main Andes.

For Chapter 3, I identified areas where bird conservation met ecosystem service protection in the Central Andes of Colombia. Inspired by the November 11th (2011) landslide event near Manizales, and the current poor results of Colombia’s Article 111 of Law 99 of 1993 as a conservation measure in this country, I set out to prioritize conservation and restoration areas where landslide prevention would complement bird conservation in the Central Andes. This area is one of the most biodiverse places on Earth, but also one of the most threatened. Using the case of the Rio Blanco Reserve, near Manizales, I identified areas for conservation where endemic and small-range bird diversity was high, and where landslide risk was also high. I further prioritized restoration areas by overlapping these conservation priorities with a forest cover map. Restoring forests in bare areas of high landslide risk and important bird diversity yields benefits for both biodiversity and people. I developed a simple landslide susceptibility model using slope, forest cover, aspect, and stream proximity. Using publicly available bird range maps, refined by elevation, I mapped concentrations of endemic and small-range bird species. I identified 1.54 km2 of potential restoration areas in the Rio Blanco Reserve, and 886 km2 in the Central Andes region. By prioritizing these areas, I facilitate the application of Article 111 which requires local and regional governments to invest in land purchases for the conservation of watersheds.

Chapter 4 dealt with elevational ranges of montane birds and the impact of lowland deforestation on their ranges in the Western Andes of Colombia, an important biodiversity hotspot. Using point counts and mist-nets, I surveyed six altitudinal transects spanning 2200 to 2800m. Three transects were forested from 2200 to 2800m, and three were partially deforested with forest cover only above 2400m. I compared abundance-weighted mean elevation, minimum elevation, and elevational range width. In addition to analyzing the effect of deforestation on 134 species, I tested its impact within trophic guilds and habitat preference groups. Abundance-weighted mean and minimum elevations were not significantly different between forested and partially deforested transects. Range width was marginally different: as expected, ranges were larger in forested transects. Species in different trophic guilds and habitat preference categories showed different trends. These results suggest that deforestation may affect species’ elevational ranges, even within the forest that remains. Climate change will likely exacerbate harmful impacts of deforestation on species’ elevational distributions. Future conservation strategies need to account for this by protecting connected forest tracts across a wide range of elevations.

In Chapter 5, I refine the ranges of 726 species from six biodiversity hotspots by suitable elevation and habitat. This set of 172 bird species for the Atlantic Forest, 138 for Central America, 100 for the Western Andes of Colombia, 57 for Madagascar, 102 for Sumatra, and 157 for Southeast Asia met the criteria for range size, endemism, threat, and forest use. Of these 586 species, the Red List deems 108 to be threatened: 15 critically endangered, 29 endangered, and 64 vulnerable. When ranges are refined by elevational limits and remaining forest cover, 10 of those critically endangered species have ranges < 100km2, but then so do 2 endangered species, seven vulnerable, and eight non-threatened ones. Similarly, 4 critically endangered species, 20 endangered, and 12 vulnerable species have refined ranges < 5000km2, but so do 66 non-threatened species. A striking 89% of these species I have classified in higher threat categories have <50% of their refined ranges inside protected areas. I find that for 43% of the species I assessed, refined range sizes fall within thresholds that typically have higher threat categories than their current assignments. I recommend these species for closer inspection by those who assess risk. These assessments are not only important on a species-by-species basis, but by combining distributions of threatened species, I create maps of conservation priorities. They differ significantly from those created from unrefined ranges.

Field data, numerical simulations and probability analyses to assess lava flow hazards at Mount Etna

Improving lava flow hazard assessment is one of the most important and challenging fields of volcanology, and has an immediate and practical impact on society. Here, we present a methodology for the quantitative assessment of lava flow hazards based on a combination of field data, numerical simulations and probability analyses. With the extensive data available on historic eruptions of Mt. Etna, going back over 2000 years, it has been possible to construct two hazard maps, one for flank and the other for summit eruptions, allowing a quantitative analysis of the most likely future courses of lava flows. The effective use of hazard maps of Etna may help in minimizing the damage from volcanic eruptions through correct land use in densely urbanized area with a population of almost one million people. Although this study was conducted on Mt. Etna, the approach used is designed to be applicable to other volcanic areas.

Achievable rates and outage probability of cognitive radio with dynamic frequency hopping under imperfect spectrum sensing

In this study, the authors propose simple methods to evaluate the achievable rates and outage probability of a cognitive radio (CR) link that takes into account the imperfectness of spectrum sensing. In the considered system, the CR transmitter and receiver correlatively sense and dynamically exploit the spectrum pool via dynamic frequency hopping. Under imperfect spectrum sensing, false-alarm and miss-detection occur which cause impulsive interference emerged from collisions due to the simultaneous spectrum access of primary and cognitive users. That makes it very challenging to evaluate the achievable rates. By first examining the static link where the channel is assumed to be constant over time, they show that the achievable rate using a Gaussian input can be calculated accurately through a simple series representation. In the second part of this study, they extend the calculation of the achievable rate to wireless fading environments. To take into account the effect of fading, they introduce a piece-wise linear curve fitting-based method to approximate the instantaneous achievable rate curve as a combination of linear segments. It is then demonstrated that the ergodic achievable rate in fast fading and the outage probability in slow fading can be calculated to achieve any given accuracy level.

Posterior Probability Modeling and Image Classification for Archaeological Site Prospection: Building a Survey Efficacy Model for Identifying Neolithic Felsite Workshops in the Shetland Islands

The application of custom classification techniques and posterior probability modeling (PPM) using Worldview-2 multispectral imagery to archaeological field survey is presented in this paper. Research is focused on the identification of Neolithic felsite stone tool workshops in the North Mavine region of the Shetland Islands in Northern Scotland. Sample data from known workshops surveyed using differential GPS are used alongside known non-sites to train a linear discriminant analysis (LDA) classifier based on a combination of datasets including Worldview-2 bands, band difference ratios (BDR) and topographical derivatives. Principal components analysis is further used to test and reduce dimensionality caused by redundant datasets. Probability models were generated by LDA using principal components and tested with sites identified through geological field survey. Testing shows the prospective ability of this technique and significance between 0.05 and 0.01, and gain statistics between 0.90 and 0.94, higher than those obtained using maximum likelihood and random forest classifiers. Results suggest that this approach is best suited to relatively homogenous site types, and performs better with correlated data sources. Finally, by combining posterior probability models and least-cost analysis, a survey least-cost efficacy model is generated showing the utility of such approaches to archaeological field survey.