Analysis of Fourier transform valuation formulas and applications

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ

German Cranial Reconstruction Registry (GCRR): protocol for a prospective, multicentre, open registry

Introduction: Owing to increasing numbers of decompressive craniectomies in patients with malignant middle cerebral artery infarction, cranioplastic surgery becomes more relevant. However, the current literature mainly consists of retrospective single-centre (evidence class III) studies. This leads to a wide variability of technical approaches and clinical outcomes. To improve our knowledge about the key elements of cranioplasty, which may help optimising clinical treatment and long-term outcome, a prospective multicentre registry across Germany, Austria and Switzerland will be established. Methods: All patients undergoing cranioplastic surgery in participating centres will be invited to join the registry. Technical methods, materials, medical history, adverse events and clinical outcome measures, including modified Rankin scale and EQ-5D, will be assessed at several time points. Patients will be accessible to inclusion either at initial decompressive surgery or when cranioplasty is planned. Scheduled monitoring will be carried out at time of inclusion and subsequently at time of discharge, if any readmission is necessary, and at follow-up presentation. Cosmetic results and patient satisfaction will also be assessed. Collected data will be managed and statistically analysed by an independent biometric institute. The primary endpoint will be mortality, need for operative revision and neurological status at 3 months following cranioplasty. Ethics and dissemination: Ethics approval was obtained at all participating centres. The registry will provide reliable prospective evidence on surgical techniques, used materials, adverse events and functional outcome, to optimise patient treatment. We expect this study to give new insights in the treatment of skull defects and to provide a basis for future evidence-based therapy regarding cranioplastic surgery. Trial registration number: This trial is indexed in the German Clinical Trials Register (DRKS-ID: DRKS00007931). The Universal Trial Number (UTN) is U1111-1168-7425

Consensus-based recommendations for diagnosis and surgical management of cranioplasty and post-traumatic hydrocephalus from a European panel

Introduction: Planning cranioplasty (CPL) in patients with suspected or proven post-traumatic hydrocephalus (PTH) poses a significant management challenge due to a lack of clear guidance. Research question: This project aims to create a European document to improve adherence and adapt to local protocols based on available resources and national health systems. Methods: After a thorough non-systematic review, a steering committee (SC) formed a European expert panel (EP) for a two-round questionnaire using the Delphi method. The questionnaire employed a 9-point Likert scale to assess the appropriateness of statements inherent to two sections: “Diagnostic criteria for PTH” and “Surgical strategies for PTH and cranial reconstruction.” Results: The panel reached a consensus on 29 statements. In the “Diagnostic criteria for PTH” section, five statements were deemed “appropriate” (consensus 74.2−90.3 %), two were labeled “inappropriate,” and seven were marked as “uncertain.” In the “Surgical strategies for PTH and cranial reconstruction” section, four statements were considered “appropriate” (consensus 74.2−90.4 %), six were “inappropriate,” and five were “uncertain.” Discussion and conclusion: Planning a cranioplasty alongside hydrocephalus remains a significant challenge in neurosurgery. Our consensus conference suggests that, in patients with cranial decompression and suspected hydrocephalus, the most suitable diagnostic approach involves a combination of evolving clinical conditions and neuroradiological imaging. The recommended management sequence prioritizes cranial reconstruction, with the option of a ventriculoperitoneal shunt when needed, preferably with a programmable valve. We strongly recommend to adopt local protocols based on expert consensus, such as this, to guide patient care