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We develop a dynamic model to study the systemic risk of the banking network, so as to study the dynamics of bank defaults. In contrast to the existing literature, we show that while the possibility of contagion is determined by interconnectedness of the financial network, whether a financial crisis can occur depends on the profile of the liquid assets of the banks in the system. Based on the dynamic model, we introduce a time to crisis index that allows us to predict the occurrence of a financial crisis. We then provide an intuitive measure of systemic risk. To illustrate the potential usefulness of our model, we provide an analysis of the system of twenty‐two German banks. We show how many of the banks are fundamentally weak, where the contagion effect may arise from, how strong the contagion effect is, and how significant the systemic risk is.

Objectives:The objectives of this study were (1) to develop and validate a simulation model to estimate daily probabilities of healthcare-associated infections (HAIs), length of stay (LOS), and mortality using time varying patient- and unit-level factors including staffing adequacy and (2) to examine whether HAI incidence varies with staffing adequacy.Setting:The study was conducted at 2 tertiary- and quaternary-care hospitals, a pediatric acute care hospital, and a community hospital within a single New York City healthcare network.Patients:All patients discharged from 2012 through 2016 (N = 562,435).Methods:We developed a non-Markovian simulation to estimate daily conditional probabilities of bloodstream, urinary tract, surgical site, and Clostridioides difficile infection, pneumonia, length of stay, and mortality. Staffing adequacy was modeled based on total nurse staffing (care supply) and the Nursing Intensity of Care Index (care demand). We compared model performance with logistic regression, and we generated case studies to illustrate daily changes in infection risk. We also described infection incidence by unit-level staffing and patient care demand on the day of infection.Results:Most model estimates fell within 95% confidence intervals of actual outcomes. The predictive power of the simulation model exceeded that of logistic regression (area under the curve [AUC], 0.852 and 0.816, respectively). HAI incidence was greatest when staffing was lowest and nursing care intensity was highest.Conclusions:This model has potential clinical utility for identifying modifiable conditions in real time, such as low staffing coupled with high care demand.

We develop a continuous-time control approach to optimal trading in a Proof-of-Stake (PoS) blockchain, formulated as a consumption-investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equations. When the utility functions are linear or convex, we derive close-form solutions and show that the bang-bang strategy is optimal (i.e., always buy or sell at full capacity). Furthermore, we bring out the explicit connection between the rate of return in trading/holding stakes and the participant's risk-adjusted valuation of the stakes. In particular, we show when a participant is risk-neutral or risk-seeking, corresponding to the risk-adjusted valuation being a martingale or a sub-martingale, the optimal strategy must be to either buy all the time, sell all the time, or first buy then sell, and with both buying and selling executed at full capacity. We also propose a risk-control version of the consumption-investment problem; and for a special case, the ''stake-parity'' problem, we show a mean-reverting strategy is optimal., Comment: 24 pages, 4 figures. This paper is published by https://onlinelibrary.wiley.com/doi/full/10.1111/mafi.12403