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.

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.)

Transferring control demands across incidental learning tasks - Stronger sequence usage in serial reaction task after shortcut option in letter string checking

After incidentally learning about a hidden regularity, participants can either continue to solve the task as instructed or, alternatively, apply a shortcut. Past research suggests that the amount of conflict implied by adopting a shortcut seems to bias the decision for vs. against continuing instruction-coherent task processing. We explored whether this decision might transfer from one incidental learning task to the next. Theories that conceptualize strategy change in incidental learning as a learning-plus-decision phenomenon suggest that high demands to adhere to instruction-coherent task processing in Task 1 will impede shortcut usage in Task 2, whereas low control demands will foster it. We sequentially applied two established incidental learning tasks differing in stimuli, responses and hidden regularity (the alphabet verification task followed by the serial reaction task, SRT). While some participants experienced a complete redundancy in the task material of the alphabet verification task (low demands to adhere to instructions), for others the redundancy was only partial. Thus, shortcut application would have led to errors (high demands to follow instructions). The low control demand condition showed the strongest usage of the fixed and repeating sequence of responses in the SRT. The transfer results are in line with the learning-plus-decision view of strategy change in incidental learning, rather than with resource theories of self-control.

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.

Structured sparsity for spatially coherent fibre orientation estimation in diffusion MRI.

We propose a novel formulation to solve the problem of intra-voxel reconstruction of the fibre orientation distribution function (FOD) in each voxel of the white matter of the brain from diffusion MRI data. The majority of the state-of-the-art methods in the field perform the reconstruction on a voxel-by-voxel level, promoting sparsity of the orientation distribution. Recent methods have proposed a global denoising of the diffusion data using spatial information prior to reconstruction, while others promote spatial regularisation through an additional empirical prior on the diffusion image at each q-space point. Our approach reconciles voxelwise sparsity and spatial regularisation and defines a spatially structured FOD sparsity prior, where the structure originates from the spatial coherence of the fibre orientation between neighbour voxels. The method is shown, through both simulated and real data, to enable accurate FOD reconstruction from a much lower number of q-space samples than the state of the art, typically 15 samples, even for quite adverse noise conditions.

Pathogenic attack and carbon reallocation in soybean leaves (Glycine max. L.): Reinitiation of the glyoxylate cycle as a defence reaction

Pathogenic attack by the fungus Botrytis cinerea (primary pathogen) on soybean leaves (Glycine max. L.; cv. Maple arrow) results in a hypersensitive response (necrotising infected leaves), in the establishment of local acquired resistance, as well as in the systemic induction of genes coding for pathogenesis-related proteins. It now appears that, concomitantly with these already well documented defence reactions, the pathogenic attack also induces the carbon reallocation mechanism based on the reinitiation of the glyoxylate cycle (pseudo-senescence of the infected leaves).

Intraosseous migration of tendinous calcifications: cortical erosions, subcortical migration and extensive intramedullary diffusion, a SIMS series.

Calcium hydroxyapatite crystal deposition is a common disorder, which sometimes causes acute pain as calcifications dissolve and migrate into adjacent soft tissue. Intraosseous calcium penetration has also been described. We illustrate the appearance of these lesions using a series of 35 cases compiled by members of the French Society of Musculoskeletal Imaging (Société d'Imagerie Musculo-Squelettique, SIMS). The first group in our series (7 cases) involved calcification-related cortical erosions of the humeral and femoral diaphyses, in particular at the pectoralis major and gluteus maximus insertions. A second group (28 cases) involved the presence of calcium material in subcortical areas. The most common site was the greater tubercle of the humerus, accompanying a calcifying tendinopathy of the supraspinatus. In addition, an extensive intramedullary diffusion of calcium deposits was observed in four of these cases, associated with cortical erosion in one case and subcortical lesions in three cases. Cortical erosions and intraosseous migration of calcifications associated with calcific tendinitis may be confused with neoplasm or infection. It is important to recognize atypical presentations of hydroxyapatite deposition to avoid unnecessary investigation or surgery.