Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedging

We prove results on bounded solutions to backward stochastic equations driven by random measures. Those bounded BSDE solutions are then applied to solve different stochastic optimization problems with exponential utility in models where the underlying filtration is noncontinuous. This includes results on portfolio optimization under an additional liability and on dynamic utility indifference valuation and partial hedging in incomplete financial markets which are exposed to risk from unpredictable events. In particular, we characterize the limiting behavior of the utility indifference hedging strategy and of the indifference value process for vanishing risk aversion.Comment: Published at http://dx.doi.org/10.1214/105051606000000475 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Scaling of singular structures in extensional flow of dilute polymer solutions

Recently singular solutions have been discovered in purely elongational flows of visco-elastic fluids. We surmise that these solutions are the mathematical structures underlying the so-called birefringent strands seen experimentally. In order to facilitate future experimental studies of these we derive a number of asymptotic results for the scaling of the width and extension of the near-singular structures in the FENE-P model for polymers of finite extensibility.Comment: 16 pages, 8 figure

Hedging with transient price impact for non-covered and covered options

We solve the superhedging problem for European options in a market with finite liquidity where trading has transient impact on prices, and possibly a permanent one in addition. Impact is multiplicative to ensure positive asset prices. Hedges and option prices depend on the physical and cash delivery specifications of the option settlement. For non-covered options, where impact at the inception and maturity dates matters, we characterize the superhedging price as a viscosity solution of a degenerate semilinear pde that can have gradient constraints. The non-linearity of the pde is governed by the transient nature of impact through a resilience function. For covered options, the pricing pde involves gamma constraints but is not affected by transience of impact. We use stochastic target techniques and geometric dynamic programming in reduced coordinates

Early Multi-organ Point-of-Care Ultrasound Evaluation of Respiratory Distress During SARS-CoV-2 Outbreak: Case Report

Introduction: Coronavirus disease 2019 (COVID-19) is caused by the virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2).  Several case series from Italy and China have highlighted the lung ultrasound findings of this disease process and may demonstrate its clinical utility during the current pandemic.Case Report: We present a case of a COVID-19 patient who presented to the emergency department twice within a 24-hour period with rapidly progressing illness. A multi-organ point-of-care ultrasound (POCUS) evaluation was used on the return visit and assisted clinical decision-making.Discussion: A multi-organ POCUS exam allows for quick assessment of acute dyspnea in the emergency department. As the lung involvement of COVID-19 is primarily a peripheral process it is readily identifiable via lung ultrasound. We believe that when applied efficiently and safely a POCUS exam can reduce clinical uncertainty and potentially limit the use of other imaging modalities when treating patients with COVID-19.Conclusion: This case highlights the utility of an early multiorgan point-of-care assessment for patients presenting with moderate respiratory distress during the severe SARS-CoV-2 pandemic