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

## TL;DR

This paper presents a general solution for stochastic convex function minimization with stochastic constraints, extending to sigma-finite measures and providing various applications.

## Contribution

It introduces a comprehensive framework for stochastic convex optimization with constraints, accommodating dependencies and general measure spaces.

## Key findings

- Solution to stochastic convex minimization with constraints
- Extension to sigma-finite measures and dependent processes
- Applications across different stochastic process scenarios

## Abstract

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.