Nonlinear Parabolic Equations arising in Mathematical Finance

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387

Variation in care in the management of children with Crohn's disease: Data from a multicenter inception cohort study

Background: Variation in care is common in medical practice. Reducing variation in care is shown to improve quality and increase favorable outcomes in chronic diseases. We sought to identify factors associated with variation in care in children with newly diagnosed Crohn's disease (CD). Methods: Prospectively collected data from a 28-site multicenter inception CD cohort were analyzed for variations in diagnostic modalities, treatment, and follow-up monitoring practices, along with complicated disease outcomes over 3 years in 1046 children. Generalized linear mixed effects models were used to investigate the intercenter variations in each outcome variable. Results: The mean age at diagnosis was 12 years, and 25.9% were nonwhite. The number of participants ranged from 5 to 112 per site. No variation existed in the initial diagnostic approach. When medication exposure was analyzed, steroid exposure varied from 28.6% to 96.9% (P 0.99). Use of immunomodulators (IMs) varied among centers both within 90 days (P < 0.01) and during 3 years of follow-up (P < 0.01). A significant variation was seen at the geographic level with follow-up small bowel imaging and colonoscopy surveillance after initial therapy. Conclusions: Intercenter variation in care was seen with the initial use of steroids and anti-TNF, but there was no difference in total 3-year exposure to these drugs. Variation in the initiation and long-term use of IMs was significant among sites, but further research with objective measures is needed to explain this variation of care. Small bowel imaging or repeat colonoscopy in CD patients was not uniformly performed across sites. As our data show the widespread existence of variation in care and disease monitoring at geographic levels among pediatric CD patients, future implementation of various practice strategies may help reduce the variation in care

The Global Invertebrate Genomics Alliance (GIGA): developing community resources to study diverse invertebrate genomes

Over 95% of all metazoan (animal) species comprise the invertebrates, but very few genomes from these organisms have been sequenced. We have, therefore, formed a Global Invertebrate Genomics Alliance (GIGA). Our intent is to build a collaborative network of diverse scientists to tackle major challenges (e.g., species selection, sample collection and storage, sequence assembly, annotation, analytical tools) associated with genome/transcriptome sequencing across a large taxonomic spectrum. We aim to promote standards that will facilitate comparative approaches to invertebrate genomics and collaborations across the international scientific community. Candidate study taxa include species from Porifera, Ctenophora, Cnidaria, Placozoa, Mollusca, Arthropoda, Echinodermata, Annelida, Bryozoa, and Platyhelminthes, among others. GIGA will target 7000 noninsect/nonnematode species, with an emphasis on marine taxa because of the unrivaled phyletic diversity in the oceans. Priorities for selecting invertebrates for sequencing will include, but are not restricted to, their phylogenetic placement; relevance to organismal, ecological, and conservation research; and their importance to fisheries and human health. We highlight benefits of sequencing both whole genomes (DNA) and transcriptomes and also suggest policies for genomic-level data access and sharing based on transparency and inclusiveness. The GIGA Web site (http://giga.nova.edu) has been launched to facilitate this collaborative venture

Viscosity Solutions to Delay Differential Equations in Demo-Economy

Economic and demographic models governed by linear delay differential equations are expressed as optimal control problems in infinite dimensions. A general objective function is considered and the concavity of the Hamiltonian is not required. The value function is a viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation and a verification theorem is proved.delay differential equation, vintage models, viscosity solutions,