Minimizing a stochastic convex function subject to stochastic constraints and some applications

In the simplest case, we obtain a general solution to a problem of minimizing an integral of a nondecreasing right continuous stochastic process from zero to some nonnegative random variable tau, under the constraints that for some nonnegative random variable T, tau is between zero and T a.s. and the expected value of tau is some alpha. The nondecreasing process and T are allowed to be dependent. In fact a more general setup involving sigma-finite measures, rather than just probability measures is considered and some consequences for families of stochastic processes are given as special cases. Various applications are provided.

No reviews yet.

No comments yet.