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Full-Text Articles in Physical Sciences and Mathematics
Optimal Stopping Problems For A Family Of Continuous-Time Markov Processes, Héctor Jasso-Fuentes, Jose-Luis Menaldi, Fidel Vásquez-Rojas
Optimal Stopping Problems For A Family Of Continuous-Time Markov Processes, Héctor Jasso-Fuentes, Jose-Luis Menaldi, Fidel Vásquez-Rojas
Mathematics Faculty Research Publications
In this paper we study the well-know optimal stopping problem applied to a general family of continuous-time Markov process. The approach to follow is merely analytic and it is based on the characterization of stopping problems through the study of a certain variational inequality; namely one solution of this inequality will coincide with the optimal value of the stopping problem. In addition, by means of this characterization, it is possible to find the so-named continuation region, and as a byproduct obtaining the optimal stopping time. The most of the material is based on the semigroup theory, infinitesimal generators and resolvents. …
Optimal Starting-Stopping Problems For Markov-Feller Processes, Jose-Luis Menaldi, Maurice Robin, Min Sun
Optimal Starting-Stopping Problems For Markov-Feller Processes, Jose-Luis Menaldi, Maurice Robin, Min Sun
Mathematics Faculty Research Publications
By means of nested inequalities in semigroup form we give a characterization of the value functions of the starting-stopping problem for general Markov-Feller processes. Next, we consider two versions of constrained problems on the nal state or on the final time. The plan is as follows:
- Introduction
- Nested variational inequalities
- Solution of optimal starting-stopping problem
- Problems with constraints
References.
On The Numerical Approximations Of An Optimal Correction Problem, M. C. Bancora-Imbert, P. L. Chow, J. L. Menaldi
On The Numerical Approximations Of An Optimal Correction Problem, M. C. Bancora-Imbert, P. L. Chow, J. L. Menaldi
Mathematics Faculty Research Publications
The numerical solution of an optimal correction problem for a damped random linear oscillator is studied. A numerical algorithm for the discretized system of the associated dynamic programming equation is given. To initiate the computation, we adopt a numerical scheme derived from the deterministic version of the problem. Next, a correction-type algorithm based on a discrete maximum principle is introduced to ensure the convergence of the iteration procedure.