The Riccati Equation in Mathematical Finance

AbstractThis paper uses ideas from symbolic computation to classify solutions to an important class of problems in mathematical finance and thus provides a linkage between these two fields. We show that Kovacic’s concept of closed-form solutions to the Riccati ordinary differential equation can be used to provide a precise mathematical definition that is useful in certain financial models. We extend this definition to a broader class of problems and discuss how these ideas can be usefully applied to practical problems in the finance area. We provide a specific application by developing a new implementation of the Cox–Ingersoll–Ross interest-rate model that may be of practical interest

Collaborative Cohort of Cohorts for COVID-19 Research (C4R) Study: Study Design

The Collaborative Cohort of Cohorts for COVID-19 Research (C4R) is a national prospective study of adults comprising 14 established US prospective cohort studies. Starting as early as 1971, investigators in the C4R cohort studies have collected data on clinical and subclinical diseases and their risk factors, including behavior, cognition, biomarkers, and social determinants of health. C4R links this pre-coronavirus disease 2019 (COVID-19) phenotyping to information on severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection and acute and postacute COVID-related illness. C4R is largely population-based, has an age range of 18-108 years, and reflects the racial, ethnic, socioeconomic, and geographic diversity of the United States. C4R ascertains SARS-CoV-2 infection and COVID-19 illness using standardized questionnaires, ascertainment of COVID-related hospitalizations and deaths, and a SARS-CoV-2 serosurvey conducted via dried blood spots. Master protocols leverage existing robust retention rates for telephone and in-person examinations and high-quality event surveillance. Extensive prepandemic data minimize referral, survival, and recall bias. Data are harmonized with research-quality phenotyping unmatched by clinical and survey-based studies; these data will be pooled and shared widely to expedite collaboration and scientific findings. This resource will allow evaluation of risk and resilience factors for COVID-19 severity and outcomes, including postacute sequelae, and assessment of the social and behavioral impact of the pandemic on long-term health trajectories

Option Replication in Discrete Time with Transaction Costs

Option replication is discussed in a discrete‐time framework with transaction costs. The model represents an extension of the Cox‐Ross‐Rubinstein binomial option pricing model to cover the case of proportional transaction costs. The method proceeds by constructing the appropriate replicating portfolio at each trading interval. Numerical values of these prices are presented for a range of parameter values. The paper derives a simple Black‐Scholes type approximation for the option prices with transaction costs and demonstrates numerically that it is quite accurate for plausible parameter values. 1992 The American Finance Associatio