in this paper, the exp-function method, with the aid of a symbolic computation system such as maple, is applied to the (2+1) -dimensional calogero bogoyavlanskii schiff equation. exact and explicit generalized solitary solutions are obtained in more general forms. the free parameters can be determined by initial or boundary conditions. the method is straightforward and concise, and its applicat...

The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval (possibly unknown) minimizing a cost functional, while satisfying hard constraints on the input. For linear systems the solution of the problem often relies upon the use of bang-bang control signals. For nonlinear systems the “shape” of the optima...

We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is well-known that HJB equations suffer the so called curse of dimensionality and, therefore, a reduction of the dimension of the system is mandatory. In this repor...

We study a class of optimal control problems with state constraints, where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to build, see [1, 2, 26]. We embed the problem in a suitable Hilbert space H and consider the associated Hamilton-Jacobi-Bellman (HJB) equation. This kind of infi...

Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style an option price constructed as a difference certainty equivalents value functions solving HJB equations. We introduce transformation method for penalized nonlinear partial differential equation. transformed equation involves possibly non-constant risk aversi...

We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain. We reduce the partially observed stochastic control problem to a complete observati...

Errata: Stochastic Optimal Control with Delay in the I: Solving HJB Equation through Partial Smoothing, and II: Verification Theorem Feedbacks

First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximat...

5 We determine the optimal dynamic investment policy for a mean quadratic variation ob6 jective function by numerical solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) partial 7 differential equation (PDE). We compare the efficient frontiers and optimal investment poli8 cies for three mean variance like strategies: pre-commitment mean variance, time-consistent 9 mean variance, and mean quad...