A Mathematical Approach to Order Book Modeling

Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional continuous-time Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence towards it. We also prove, by means of the functional central limit theorem (FCLT), that the rescaled-centered price process converges to a Brownian motion. We illustrate the analysis with numerical simulation and comparison against market data

Effects of a short residential thermal spa program to prevent work-related stress/burnout on stress biomarkers: The thermstress proof of concept study

Objective Work-related stress is a public health issue. Stress has multiple physical and psychological consequences, the most serious of which are increased mortality and cardiovascular morbidity. The ThermStress protocol was designed to offer a short residential thermal spa program for work-related stress prevention that is compatible with a professional context. Methods Participants will be 56 male and female workers aged 18 years or above. All participants will undergo a 6-day residential spa program comprising psychological intervention, physical activity, thermal spa treatment, health education, eating disorder therapy and a follow-up. On six occasions, participants’ heart rate variability, cardiac remodelling and function, electrodermal activity, blood markers, anthropometry and body composition, psychology and quality of life will be measured using questionnaires and bone parameters. Results This study protocol reports the planned and ongoing research for this intervention. Discussion The ThermStress protocol has been approved by an institutional ethics committee (ANSM: 2016 A02082 49). It is expected that this proof of concept study will highlight the effect of a short-term specific residential thermal spa program on the prevention of occupational burnout and work-related stress. The findings will be disseminated at several research conferences and in published articles in peer-reviewed journals. Trial Registration: ClinicalTrials.gov (NCT 03536624, 24/05/2018

On the wellposedness of some McKean models with moderated or singular diffusion coefficient

We investigate the well-posedness problem related to two models of nonlinear McKean Stochastic Differential Equations with some local interaction in the diffusion term. First, we revisit the case of the McKean-Vlasov dynamics with moderate interaction, previously studied by Meleard and Jourdain in [16], under slightly weaker assumptions, by showing the existence and uniqueness of a weak solution using a Sobolev regularity framework instead of a Holder one. Second, we study the construction of a Lagrangian Stochastic model endowed with a conditional McKean diffusion term in the velocity dynamics and a nondegenerate diffusion term in the position dynamics

Etude d'un probleme de controle optimal convexe mal pose

SIGLECNRS T 60080 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc