We propose a general framework for intra-day trading based on the control of trading algorithms. Given a generic parameterized algorithm, we control the dates (τi)i at which it is launched, the length (δi)i of the trading period and the value of the parameters (Ei)i kept during the time interval [τi, τi + δi[. This gives rise to a non-classical impulse control problem where not only the regime ...

A utility maximization problem in an illiquid market is studied. The financial market is assumed to have temporary price impact with finite resilience. After the formulation of this problem as a Markovian stochastic optimal control problem a dynamic programming approach is used for its analysis. In particular, the dynamic programming principle is proved and the value function is shown to be the...

We prove a theorem of existence of time-optimal curves in the space of probability measures, a Dynamic Programming Principle, a controllability result and some comparisons between the classical and the generalized framework. A proper definition of viscosity solution, together with some approximation results, leaded us to prove that the generalization of the minimum time function solves a suitab...

We discuss a class of time-dependent Hamilton-Jacobi equations, where an unknown function of time is intended to keep the maximum of the solution to the constant value 0. Our main result is that the full problem has a unique viscosity solution, which is in fact classical. The motivation is a selection-mutation model which, in the limit of small diffusion, exhibits concentration on the zero leve...

We study the Bellman equation for undiscounted exit time optimal control problems for nonlinear systems and nonnegative instantaneous costs using the dynamic programming approach. Using viscosity solution theory, we prove a uniqueness theorem that characterizes the value functions for these problems as the unique viscosity solutions of the corresponding Bellman equations that satisfy appropriat...

We study an innnite horizon optimal control problem for a system with two state variables. One of them has the evolution governed by a controlled ordinary diierential equation and the other one is related to the latter by a hysteresis relation, represented here by either a play operator or a Prandtl-Ishlinskii operator. By dynamic programming, we derive the corresponding (discontinuous) rst ord...

With the aim of locating the origin of discrepancy between experimental and computer simulation results on bulk viscosity of liquid argon, a molecular dynamic simulation of argon interacting via ab initio pair potential and triple-dipole three-body potential has been undertaken. Bulk viscosity, obtained using Green-Kubo formula, is different from the values obtained from modeling argon using Le...

A shock-like structure appears in a time-averaged pattern produced by the Kuramoto-Sivashinsky equation and the noisy Burgers equation with fixed boundary conditions. We show that the effective viscosity computed from the width of the time-averaged shock structure is consistent with that computed from the time correlation of the fluctuations. The effective viscosity depends on the lengthscale, ...

The static and dynamic (complex) shear viscosity of a single-layer dusty plasma is measured by applying, respectively, a stationary and a periodically modulated shear stress, induced by the light pressure of manipulating laser beams. Under static conditions we observe a decrease of the viscosity with increasing shear rate, the so-called shear-thinning behavior. Under oscillating shear both the ...

This study is carried out to explore the effect of nano materials (SiO2 & TiO2) on the physical and rheological properties of Bitumen. To achieve this goal, Nano materials are blended in bitumen in various percentages (0.3, 0.6, 0.9 and 1.2%). The physical and rheological properties of modified binders are characterized using a penetration, softening point, kinematic viscosity and a dynamic...