Consider a company whose business carries the potential for investment losses and is additionally vulnerable to exogenous shocks. The unpredictability of the shocks makes it challenging for both the company and the regulator to accurately assess their impact, potentially leading to an underestimation of solvency capital when employing traditional approaches. In this paper, we utilize a stylized model to conduct an extreme value analysis of the tail risk of the company under a Fréchet-type and a Gumbel-type shock. Our main results explicitly demonstrate the different roles of investment risk and shock risk in driving large losses. Furthermore, we derive asymptotic estimates for the value at risk and expected shortfall of the total loss. Numerical studies are conducted to examine the accuracy of the obtained estimates.

Bogomolov and Tschinkel [‘Algebraic varieties over small fields’, Diophantine Geometry, U. Zannier (ed.), CRM Series, 4 (Scuola Normale Superiore di Pisa, Pisa, 2007), 73–91] proved that, given two complex elliptic curves $E_1$ and $E_2$ along with even degree-$2$ maps $\pi _j\colon E_j\to \mathbb {P}^1$ having different branch loci, the intersection of the image of the torsion points of $E_1$ and $E_2$ under their respective $\pi _j$ is finite. They conjectured (also in works with Fu) that the cardinality of this intersection is uniformly bounded independently of the elliptic curves. The recent proof of the uniform Manin–Mumford conjecture implies a full solution of the Bogomolov–Fu–Tschinkel conjecture. In this paper, we prove a generalisation of the Bogomolov–Fu–Tschinkel conjecture whereby, instead of even degree-$2$ maps, one can use any rational functions of bounded degree on the elliptic curves as long as they have different branch loci. Our approach combines Nevanlinna theory with the uniform Manin–Mumford conjecture. With similar techniques, we also prove a result on lower bounds for ranks of elliptic curves over number fields.

Investigating a conjecture of Zannier, we study irreducible subvarieties of abelian schemes that dominate the base and contain a Zariski dense set of torsion points that lie on pairwise isogenous fibers. If everything is defined over the algebraic numbers and the abelian scheme has maximal variation, we prove that the geometric generic fiber of such a subvariety is a union of torsion cosets. We go on to prove fully or partially explicit versions of this result in fibered powers of the Legendre family of elliptic curves. Finally, we apply a recent result of Galateau and Martínez to obtain uniform bounds on the number of maximal torsion cosets in the Manin–Mumford problem across a given isogeny class. For the proofs, we adapt the strategy, due to Lang, Serre, Tate, and Hindry, of using Galois automorphisms that act on the torsion as homotheties to the family setting.

In multi-panelled higher jurisdictions, a larger, extended formation of judges tends to be established within the court. It bears various names: the grand chamber, the extended chamber, the expanded composition, the reunion of several chambers, a court sitting en banc, an extended section or a division of a court. In larger but not too large jurisdictions, the same role is adopted by the plenary. For ease of reference, I shall refer to all such extended judicial formations with the generic name ‘grand chamber’.

To bear the same name does not necessarily mean to perform the same function. As a Czech lawyer, I have always intuitively assumed that the role of such a body within an apex court is to unify the case law. In the Czech Republic, as well as in a number of other supreme continental jurisdictions for that matter, there tends to be only one reason for the presence of a grand chamber within a supreme court: to unify the diverging lines of case law and to set a clear line of precedent. However, that has never really been the job description, least of all the practice, of the Grand Chamber of the Court of Justice of the European Union (‘Court’). This begs the question: what may then be other structural reasons for the existence of such a body within an apex jurisdiction? What is the specific role, function, and ensuing justification for the Grand Chamber of the Court?

This article offers some personal reflections on that question. It is structured as follows: it begins with a short comparative overview of some of the grand chambers within European (national) courts, overseas in the common law world, as well as at the European Court of Human Rights, in order to tease out the functional rationale for various types of extended judicial compositions within those systems (Part I). Next, two types of such functional justifications for grand chambers in the form of ideal models are identified (Part II). Finally, those justifications are then considered in light of the legislative design and the current practice of the Grand Chamber of the Court, before concluding with two modest suggestions (Part III).

Let $\mathbf{M}=(M_{1},\ldots ,M_{k})$ be a tuple of real $d\times d$ matrices. Under certain irreducibility assumptions, we give checkable criteria for deciding whether $\mathbf{M}$ possesses the following property: there exist two constants $\unicode[STIX]{x1D706}\in \mathbb{R}$ and $C>0$ such that for any $n\in \mathbb{N}$ and any $i_{1},\ldots ,i_{n}\in \{1,\ldots ,k\}$, either $M_{i_{1}}\cdots M_{i_{n}}=\mathbf{0}$ or $C^{-1}e^{\unicode[STIX]{x1D706}n}\leq \Vert M_{i_{1}}\cdots M_{i_{n}}\Vert \leq Ce^{\unicode[STIX]{x1D706}n}$, where $\Vert \cdot \Vert$ is a matrix norm. The proof is based on symbolic dynamics and the thermodynamic formalism for matrix products. As applications, we are able to check the absolute continuity of a class of overlapping self-similar measures on $\mathbb{R}$, the absolute continuity of certain self-affine measures in $\mathbb{R}^{d}$ and the dimensional regularity of a class of sofic affine-invariant sets in the plane.

The purpose of this work was to evaluate the capacity of existing landscape irrigation equipment to deliver the expected irrigation depth at a level of uniformity that can potentially be used in a precision irrigation management environment. Popular pop-up sprayer systems from two leading manufacturers (Rain-bird and Hunter variable arc and fixed arc nozzles) were subject to spatial distribution tests, in order to establish the application patterns under ideal conditions. The results indicate that it is not possible to fully rely on the catalog application depth values, with some variable arc nozzles applying up to 200% of the catalog values. These nozzles can have low values of uniformity, with Christiansen´s uniformity coefficient, CU, of between 0.31 and 0.70, making it difficult to obtain good uniformity even under a back-to-back setting. These results indicate that variable arc nozzles are not recommended for use in precision agriculture. It is preferable to use fixed arc nozzles, after actual field evaluation.

Knowledge of weed community structure in vegetable crops of the north central region (NCR) is poor. To characterize weed species composition present at harvest (hereafter called residual weeds) in processing sweet corn, 175 fields were surveyed in Illinois, Minnesota, and Wisconsin from 2005 to 2007. Weed density was enumerated by species in thirty 1-m2 quadrats placed randomly along a 300- to 500-m loop through the field, and additional species observed outside quadrats were also recorded. Based on weed community composition, population density, and mean plant size, overall weed interference level was rated. A total of 56 residual weed species were observed and no single species dominated the community of NCR processing sweet corn. Several of the most abundant species, such as common lambsquarters and velvetleaf, have been problems for many years, while other species, like wild-proso millet, have become problematic in only the last 20 yr. Compared to a survey of weeds in sweet corn more than 40 yr ago, greater use of herbicides is associated with reductions in weed density by approximately an order of magnitude; however, 57% of fields appeared to suffer yield loss due to weeds. Sweet corn harvest in the NCR ranges from July into early October. Earlier harvests were characterized by some of the highest weed densities, while late-emerging weeds such as eastern black nightshade occurred in fields harvested after August. Fall panicum, giant foxtail, wild-proso millet, common lambsquarters, and velvetleaf were the most abundant species across the NCR, yet each state had some unique dominant weeds.

Following the Reformation, uniformity was a key principle undergirding worship in the Church of England. The Crown claimed the prerogative to order the use of, and to alter, Church services in spite of the provisions of any Act of Uniformity, the Canons or any Declaration of Assent. This caused confusion among the clergy and others as to who had ‘lawful authority’ to permit such usages or changes. This confusion was exacerbated by episcopal claims to a jus liturgicum. Statute and case law, as well as the wording of the Declaration, also ensured rigidity in doctrinal adhesion. Since the Church of England (Worship and Doctrine) Measure 1974 and recent amendments to the Canons and the Declaration of Assent, this rigidity has been relaxed and clarity provided as to who may authorise services or permit departure from otherwise authorised forms of service.

In this paper we consider some nonstandard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim size distribution belongs to some classes of heavy-tailed distributions and a constraint is imposed on the Lévy process in terms of its Laplace exponent, we obtain some asymptotic formulae for the tail probability of discounted aggregate claims and ruin probabilities holding uniformly for some finite or infinite time horizons.

Pig breeders in the past have adopted their breeding goals according to the needs of the producers, processors and consumers and have made remarkable genetic improvements in the traits of interest. However, it is becoming more and more challenging to meet the market needs and expectations of consumers and in general of the citizens. In view of the current and future trends, the breeding goals have to include several additional traits and new phenotypes. These phenotypes include (a) vitality from birth to slaughter, (b) uniformity at different levels of production, (c) robustness, (d) welfare and health and (e) phenotypes to reduce carbon footprint. Advancements in management, genomics, statistical models and other technologies provide opportunities for recording these phenotypes. These new developments also provide opportunities for making effective use of the new phenotypes for faster genetic improvement to meet the newly adapted breeding goals.

Consider a continuous-time renewal risk model with a constant force of interest. We assume that claim sizes and interarrival times correspondingly form a sequence of independent and identically distributed random pairs and that each pair obeys a dependence structure described via the conditional tail probability of a claim size given the interarrival time before the claim. We focus on determining the impact of this dependence structure on the asymptotic tail probability of discounted aggregate claims. Assuming that the claim size distribution is subexponential, we derive an exact locally uniform asymptotic formula, which quantitatively captures the impact of the dependence structure. When the claim size distribution is extended regularly varying tailed, we show that this asymptotic formula is globally uniform.

In breeding programs, robustness of animals and uniformity of end product can be improved by exploiting genetic variation in residual variance. Residual variance can be defined as environmental variance after accounting for all identifiable effects. The aims of this study were to estimate genetic variance in residual variance of body weight, and to estimate genetic correlations between body weight itself and its residual variance and between female and male residual variance for broilers. The data sets comprised 26 972 female and 24 407 male body weight records. Variance components were estimated with ASREML. Estimates of the heritability of residual variance were in the range 0.029 (s.e. = 0.003) to 0.047 (s.e. = 0.004). The genetic coefficients of variation were high, between 0.35 and 0.57. Heritabilities were higher in females than in males. Accounting for heterogeneous residual variance increased the heritabilities for body weight as well. Genetic correlations between body weight and its residual variance were −0.41 (s.e. = 0.032) and −0.45 (s.e. = 0.040), respectively, in females and males. The genetic correlation between female and male residual variance was 0.11 (s.e. = 0.089), indicating that female and male residual variance are different traits. Results indicate good opportunities to simultaneously increase the mean and improve uniformity of body weight of broilers by selection.