We consider optimal investment problems for a diffusion market model with nonobservable random drifts that evolve as an Itô’s process. Admissible strategies do not use direct observations of the market parameters, but rather use historical stock prices. For a non-linear problem with a general performance criterion, the optimal portfolio strategy is expressed via the solution of a scalar minimiz...

Window and free surface interfaces perturb the flow in compression wave experiments. The velocity of these interfaces is routinely measured in shock-compression experiments using interferometry (i.e., VISAR). Interface perturbations often must be accounted for before meaningful material property results can be obtained. For shockless experiments when stress is a single valued function of strain...

Using purely probabilistic methods, we prove the existence and uniqueness of solutions for a system coupled forward-backward stochastic differential equations (FBSDEs) with measurable, possibly discontinuous, coefficients. As corollary, obtain well-posedness semilinear parabolic partial (PDEs)Lu(t,x)+F(t,x,u,∂xu)=0;u(T,x)=h(x) in natural domain second order linear operator L when F h are not ne...

in this paper, we consider the construction of a new class ofnumerical methods based on the backward differentiation formulas(bdfs) that be equipped by including two off--step points. werepresent these methods from general linear methods (glms) pointof view which provides an easy process to improve their stabilityproperties and implementation in a variable stepsize mode. thesesuperiorities are ...

We compute conjugacy classes in maximal parabolic subgroups of the general linear group. This computation proceeds by reducing to a “matrix problem”. Such problems involve finding normal forms for matrices under a specified set of row and column operations. We solve the relevant matrix problem in small dimensional cases. This gives us all conjugacy classes in maximal parabolic subgroups over a ...

In this article we propose an efficient numerical scheme based on a Shishkin mesh for a class of singularly perturbed parabolic convection-diffusion problems with boundary turning point and retarded arguments. The solution of the considered problem exhibit a boundary layer on the left side of the domain. The continuous problem is semidiscretized by means of backward Euler finite difference meth...

In this paper, we consider an optimal control problem, which is governed by a linear parabolic equation and is subject to state constraints pointwise in time. Optimal order error estimates are developed for a space-time finite element discretization of this problem. Numerical examples confirm the theoretical results. As a byproduct of our analysis, we derive a new regularity result for the opti...

In this paper we examine the application of evolutionary algorithms to find open-loop control solutions of the optimal control problem arising from the semidiscretisation of a linear parabolic tracking problem with boundary control. The solution is compared with the solutions obtained by methods based upon the variational equations of the Minimum Principle and the finite element method.