Valuing equity-linked death benefits in jump diffusion models

The paper is motivated by the valuation problem of guaranteed minimum death benefits in various equity-linked products. At the time of death, a benefit payment is due. It may depend not only on the price of a stock or stock fund at that time, but also on prior prices. The problem is to calculate the expected discounted value of the benefit payment. Because the distribution of the time of death can be approximated by a combination of exponential distributions, it suffices to solve the problem for an exponentially distributed time of death. The stock price process is assumed to be the exponential of a Brownian motion plus an independent compound Poisson process whose upward and downward jumps are modeled by combinations (or mixtures) of exponential distributions. Results for exponential stopping of a Lévy process are used to derive a series of closed-form formulas for call, put, lookback, and barrier options, dynamic fund protection, and dynamic withdrawal benefit with guarantee. We also discuss how barrier options can be used to model lapses and surrenders.

Reduction of respiratory motion artifacts for free-breathing whole-heart coronary MRA by weighted iterative reconstruction.

PURPOSE: To combine weighted iterative reconstruction with self-navigated free-breathing coronary magnetic resonance angiography for retrospective reduction of respiratory motion artifacts. METHODS: One-dimensional self-navigation was improved for robust respiratory motion detection and the consistency of the acquired data was estimated on the detected motion. Based on the data consistency, the data fidelity term of iterative reconstruction was weighted to reduce the effects of respiratory motion. In vivo experiments were performed in 14 healthy volunteers and the resulting image quality of the proposed method was compared to a navigator-gated reference in terms of acquisition time, vessel length, and sharpness. RESULT: Although the sampling pattern of the proposed method contained 60% more samples with respect to the reference, the scan efficiency was improved from 39.5 ± 10.1% to 55.1 ± 9.1%. The improved self-navigation showed a high correlation to the standard navigator signal and the described weighting efficiently reduced respiratory motion artifacts. Overall, the average image quality of the proposed method was comparable to the navigator-gated reference. CONCLUSION: Self-navigated coronary magnetic resonance angiography was successfully combined with weighted iterative reconstruction to reduce the total acquisition time and efficiently suppress respiratory motion artifacts. The simplicity of the experimental setup and the promising image quality are encouraging toward future clinical evaluation. Magn Reson Med 73:1885-1895, 2015. © 2014 Wiley Periodicals, Inc.

Intravoxel incoherent motion diffusion-weighted imaging in the liver: comparison of mono-, bi- and tri-exponential modelling at 3.0-T.

PURPOSE: To determine whether a mono-, bi- or tri-exponential model best fits the intravoxel incoherent motion (IVIM) diffusion-weighted imaging (DWI) signal of normal livers. MATERIALS AND METHODS: The pilot and validation studies were conducted in 38 and 36 patients with normal livers, respectively. The DWI sequence was performed using single-shot echoplanar imaging with 11 (pilot study) and 16 (validation study) b values. In each study, data from all patients were used to model the IVIM signal of normal liver. Diffusion coefficients (Di ± standard deviations) and their fractions (fi ± standard deviations) were determined from each model. The models were compared using the extra sum-of-squares test and information criteria. RESULTS: The tri-exponential model provided a better fit than both the bi- and mono-exponential models. The tri-exponential IVIM model determined three diffusion compartments: a slow (D1 = 1.35 ± 0.03 × 10(-3) mm(2)/s; f1 = 72.7 ± 0.9 %), a fast (D2 = 26.50 ± 2.49 × 10(-3) mm(2)/s; f2 = 13.7 ± 0.6 %) and a very fast (D3 = 404.00 ± 43.7 × 10(-3) mm(2)/s; f3 = 13.5 ± 0.8 %) diffusion compartment [results from the validation study]. The very fast compartment contributed to the IVIM signal only for b values ≤15 s/mm(2) CONCLUSION: The tri-exponential model provided the best fit for IVIM signal decay in the liver over the 0-800 s/mm(2) range. In IVIM analysis of normal liver, a third very fast (pseudo)diffusion component might be relevant. KEY POINTS: ? For normal liver, tri-exponential IVIM model might be superior to bi-exponential ? A very fast compartment (D = 404.00 ± 43.7 × 10 (-3)  mm (2) /s; f = 13.5 ± 0.8 %) is determined from the tri-exponential model ? The compartment contributes to the IVIM signal only for b ≤ 15 s/mm (2.)

Tree cover at fine and coarse spatial grains interacts with shade tolerance to shape plant species distributions across the Alps

The role of competition for light among plants has long been recognized at local scales, but its potential importance for plant species' distribution at larger spatial scales has largely been ignored. Tree cover acts as a modulator of local abiotic conditions, notably by reducing light availability below the canopy and thus the performance of species that are not adapted to low-light conditions. However, this local effect may propagate to coarser spatial grains. Using 6,935 vegetation plots located across the European Alps, we fit Generalized Linear Models (GLM) for the distribution of 960 herbs and shrubs species to assess the effect of tree cover at both plot and landscape grain sizes (~ 10-m and 1-km, respectively). We ran four models with different combinations of variables (climate, soil and tree cover) for each species at both spatial grains. We used partial regressions to evaluate the independent effects of plot- and landscape-scale tree cover on plant communities. Finally, the effects on species' elevational range limits were assessed by simulating a removal experiment comparing the species' distribution under high and low tree cover. Accounting for tree cover improved model performance, with shade-tolerant species increasing their probability of presence at high tree cover whereas shade-intolerant species showed the opposite pattern. The tree cover effect occurred consistently at both plot and landscape spatial grains, albeit strongest at the former. Importantly, tree cover at the two grain sizes had partially independent effects on plot-scale plant communities, suggesting that the effects may be transmitted to coarser grains through meta-community dynamics. At high tree cover, shade-intolerant species exhibited elevational range contractions, especially at their upper limit, whereas shade-tolerant species showed elevational range expansions at both limits. Our findings suggest that the range shifts for herb and shrub species may be modulated by tree cover dynamics.

Diffusion-weighted MR imaging in musculoskeletal diseases: Current concepts.

MR imaging is currently regarded as a pivotal technique for the assessment of a variety of musculoskeletal conditions. Diffusion-weighted MR imaging (DWI) is a relatively recent sequence that provides information on the degree of cellularity of lesions. Apparent diffusion coefficient (ADC) value provides information on the movement of water molecules outside the cells. The literature contains many studies that have evaluated the role of DWI in musculoskeletal diseases. However, to date they yielded conflicting results on the use and the diagnostic capabilities of DWI in the area of musculoskeletal diseases. However, many of them have showed that DWI is a useful technique for the evaluation of the extent of the disease in a subset of musculoskeletal cancers. In terms of tissue characterization, DWI may be an adjunct to the more conventional MR imaging techniques but should be interpreted along with the signal of the lesion as observed on conventional sequences, especially in musculoskeletal cancers. Regarding the monitoring of response to therapy in cancer or inflammatory disease, the use of ADC value may represent a more reliable additional tool but must be compared to the initial ADC value of the lesions along with the knowledge of the actual therapy.

Back to Gondwanaland: can ancient vicariance explain (some) Indian Ocean disjunct plant distributions?

Oceans, or other wide expanses of inhospitable environment, interrupt present day distributions of many plant groups. Using molecular dating techniques, generally incorporating fossil evidence, we can estimate when such distributions originated. Numerous dating analyses have recently precipitated a paradigm shift in the general explanations for the phenomenon, away from older geological causes, such as continental drift, in favour of more recent, long-distance dispersal (LDD). For example, the 'Gondwanan vicariance' scenario has been dismissed in various studies of Indian Ocean disjunct distributions. We used the gentian tribe Exaceae to reassess this scenario using molecular dating with minimum (fossil), maximum (geological), secondary (from wider analyses) and hypothesis-driven age constraints. Our results indicate that ancient vicariance cannot be ruled out as an explanation for the early origins of Exaceae across Africa, Madagascar and the Indian subcontinent unless a strong assumption is made about the maximum age of Gentianales. However, both the Gondwanan scenario and the available evidence suggest that there were also several, more recent, intercontinental dispersals during the diversification of the group.

Comparison of accelerated T1-weighted whole-brain structural-imaging protocols.

Imaging in neuroscience, clinical research and pharmaceutical trials often employs the 3D magnetisation-prepared rapid gradient-echo (MPRAGE) sequence to obtain structural T1-weighted images with high spatial resolution of the human brain. Typical research and clinical routine MPRAGE protocols with ~1mm isotropic resolution require data acquisition time in the range of 5-10min and often use only moderate two-fold acceleration factor for parallel imaging. Recent advances in MRI hardware and acquisition methodology promise improved leverage of the MR signal and more benign artefact properties in particular when employing increased acceleration factors in clinical routine and research. In this study, we examined four variants of a four-fold-accelerated MPRAGE protocol (2D-GRAPPA, CAIPIRINHA, CAIPIRINHA elliptical, and segmented MPRAGE) and compared clinical readings, basic image quality metrics (SNR, CNR), and automated brain tissue segmentation for morphological assessments of brain structures. The results were benchmarked against a widely-used two-fold-accelerated 3T ADNI MPRAGE protocol that served as reference in this study. 22 healthy subjects (age=20-44yrs.) were imaged with all MPRAGE variants in a single session. An experienced reader rated all images of clinically useful image quality. CAIPIRINHA MPRAGE scans were perceived on average to be of identical value for reading as the reference ADNI-2 protocol. SNR and CNR measurements exhibited the theoretically expected performance at the four-fold acceleration. The results of this study demonstrate that the four-fold accelerated protocols introduce systematic biases in the segmentation results of some brain structures compared to the reference ADNI-2 protocol. Furthermore, results suggest that the increased noise levels in the accelerated protocols play an important role in introducing these biases, at least under the present study conditions.