Existence of Optimal Stochastic Controls (I). Convergence of the Finite Difference Approximations of a Discounted Problem for a Diffusion.

摘要

In part one the author gives a fairly general method for proving the existence of an optimal control for a large class of stochastic differential equation models. In part two,it is shown that the solutions to finite difference approximations to the partial differential equation converge to C(x) as the difference interval goes to zero,whether or not the derivatives actually exist. The result generalizes previous results for similar problems,and the techniques can be applied to a number of related problems. (Modified author abstract)