An Optimal Execution Problem with Market Impact

We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales, otherwise the value function is continuous. Moreover, we show the semi-group property (Bellman principle) and characterise the value function as a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of the optimal strategies change completely, depending on the amount of the trader's security holdings and where optimal strategies in the Black-Scholes type market with nonlinear market impact are not block liquidation but gradual liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal execution problem with market impact" in Finance and Stochastics (2014

Inconsistent identification of pit bull-type dogs by shelter staff

AbstractShelter staff and veterinarians routinely make subjective dog breed identification based on appearance, but their accuracy regarding pit bull-type breeds is unknown. The purpose of this study was to measure agreement among shelter staff in assigning pit bull-type breed designations to shelter dogs and to compare breed assignments with DNA breed signatures. In this prospective cross-sectional study, four staff members at each of four different shelters recorded their suspected breed(s) for 30 dogs; there was a total of 16 breed assessors and 120 dogs. The terms American pit bull terrier, American Staffordshire terrier, Staffordshire bull terrier, pit bull, and their mixes were included in the study definition of ‘pit bull-type breeds.’Using visual identification only, the median inter-observer agreements and kappa values in pair-wise comparisons of each of the staff breed assignments for pit bull-type breed vs. not pit bull-type breed ranged from 76% to 83% and from 0.44 to 0.52 (moderate agreement), respectively. Whole blood was submitted to a commercial DNA testing laboratory for breed identification. Whereas DNA breed signatures identified only 25 dogs (21%) as pit bull-type, shelter staff collectively identified 62 (52%) dogs as pit bull-type. Agreement between visual and DNA-based breed assignments varied among individuals, with sensitivity for pit bull-type identification ranging from 33% to 75% and specificity ranging from 52% to 100%. The median kappa value for inter-observer agreement with DNA results at each shelter ranged from 0.1 to 0.48 (poor to moderate). Lack of consistency among shelter staff indicated that visual identification of pit bull-type dogs was unreliable