We build a multi-stage stochastic program of an asset-liability management problem of a leasing company, analyse model results and present a stress-testing methodology suited for financial applications. At the beginning, the business model of such a company is formulated. We introduce three various risk constraints, namely the chance constraint, the Value-at-Risk constraint and the conditional Value-at-Risk constraint along with the second-order stochastic dominance constraint, which are applied to the model to control risk of the optimal strategy. We also present the structure and the generation process of our scenarios. To capture the evolution of interest rates the Hull-White model is used. Thereafter, results of the model and the effect of the risk constraints on the optimal decisions are thoroughly investigated. In the final part, the performance of the optimal solutions of the problems for unconsidered and unfavourable crisis scenarios is inspected. The methodology of a stress test we used was proposed in such a way that it answers typical questions asked by asset-liability managers.
The neutral differential equation (1.1) $$ \frac{{\mathrm{d}}^n}{{\mathrm{d}} t^n} [x(t)+x(t-\tau)] + \sigma F(t,x(g(t))) = 0, $$ is considered under the following conditions: $n\ge 2$, $\tau >0$, $\sigma = \pm 1$, $F(t,u)$ is nonnegative on $[t_0, \infty) \times (0,\infty)$ and is nondecreasing in $u\in (0,\infty)$, and $\lim g(t) = \infty$ as $t\rightarrow \infty$. It is shown that equation (1.1) has a solution $x(t)$ such that (1.2) $$ \lim_{t\rightarrow \infty} \frac{x(t)}{t^k}\ \text{exists and is a positive finite value if and only if} \int^{\infty}_{t_0} t^{n-k-1} F(t,c[g(t)]^k){\mathrm{d}} t < \infty\text{ for some }c > 0. $$ Here, $k$ is an integer with $0\le k \le n-1$. To prove the existence of a solution $x(t)$ satisfying (1.2), the Schauder-Tychonoff fixed point theorem is used.
Does there exist an atomic lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question (and slightly more) is given: An example of an atomic MV-effect algebra with a non-atomic Boolean subalgebra of sharp or central elements is presented.
Classical biological control is an important means of managing the increasing threat of invasive plants. It constitutes the introduction of natural enemies from the native range of the target plant into the invaded area. This method may be the only cost-effective solution to control the rapidly expanding common ragweed, Ambrosia artemisiifolia, in non-crop habitats in Europe. Therefore, candidate biocontrol agents urgently need to be assessed for their suitability for ragweed control in Europe. A previous literature review prioritized the host-specific leaf beetle Ophraella slobodkini as a candidate agent for ragweed control in Europe, whereas it rejected its oligophagous congener O. communa. Meanwhile, O. communa was accidentally introduced and became established south of the European Alps, and we show here that it is expanding its European range. We then present a short version of the traditional pre-release risk-benefit assessment for these two candidate agents to facilitate fast decision-making about further research efforts. We selected two complementary tests that can be conducted relatively rapidly and inform about essential risks and benefits. We conducted a comparative no-choice juvenile performance assay using leaves of ragweed and sunflower, the most important non-target plant, in Petri dishes in climatic conditions similar to that in the current European range of O. communa. This informs on the fundamental host range and potential for increasing abundance on these host plants. The results confirm that O. slobodkini does not survive on, and is hence unlikely to cause severe damage to sunflower, while O. communa can survive but develops more slowly on sunflower than on ragweed. In parallel, our species distribution models predict no suitable area for the establishment of O. slobodkini in Europe, while O. communa is likely to expand its current range to include a maximum of 18% of the European ragweed distribution. Based on this early assessment, the prioritization and further assessment of O. slobodkini seem unwarranted whereas the results urgently advocate further risk-benefit analysis of O. communa. Having revealed that most of the European area colonized by ragweed is unlikely to be suitable for these species of Ophraella we suggest the use of such relatively short and cheap preliminary assessment to prioritise other candidate agents or strains for these areas., Suzanne T. E. Lommen, Emilien F. Jolidon, Yan Sun, José I. Bustamante Eduardo, Heinz Müller-Schärer., and Obsahuje bibliografii