In this paper, we derive the optimal boundary for pair trading. This boundary defines the points of entry into or exit from the market for a given stock pair. However, if the assumed model contains uncertainty, the resulting boundary could result in large losses. To avoid this, we develop a more robust strategy by accounting for the model uncertainty. To incorporate the model uncertainty, we us...

where the functions ρ, u, θ and d represent the mass density,the velocity field, the absolute temperature and the unit vector field that represents the macroscopic molecular orientation of the liquid crystal material. P stands for the pressure, S denotes the viscous stress tensor. The positive constants ν, κ denote the competition between kinetic energy and potential energy, and microscopic ela...

We consider a multidimensional normally or obliquely reflected diffusion in smooth domain. approximate it by solutions of stochastic differential equations without reflection using the penalty method, that is, we term with an additional drift term. In existing literature, usually specific approximating sequence is provided to prove existence diffusion. this paper, provide general sufficient con...

The Sub-Mesh Penalty (SMP) method, a new fictitious domain method of high order is presented. The final aim is to develop an efficient coupling between incompressible multiphase flows and fixed or moving obstacles of complex shape. The flow is solved on a fixed Cartesian grid and the solid objects are represented by Lagrangian surface elements. Several validation problems in 2D and 3D are prese...

in this work, we study a unilateral contact problem with non local friction of coulombbetween a locking material and a rigid foundation. in the first step , we present the mathematicalmodel for a static process, we establish the variational formulation in the form of a variationalinequality and we prove the existence and uniqueness of the solution. in the second step, usingthe penalty method we...

In this work, we show quasi-optimal interface error estimates for solutions obtained by the symmetric interior penalty discontinuous Galerkin method. It is proved that the numerical solution restricted to an interface converges with order |lnh|h under suitable regularity requirements, where the logarithmic factor is only present in the lowest order case, i.e., k = 1. For this case, we also deri...

We discuss the optimality in L2 of a variant of the Incomplete Discontinuous Galerkin Interior Penalty method (IIPG) for second order linear elliptic problems. We prove optimal estimate, in two and three dimensions, for the lowest order case under suitable regularity assumptions on the data and on the mesh. We also provide numerical evidence, in one dimension, of the necessity of the regularity...