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 τ, under the constraints that for some nonnegative random variable T, τ∈[0,T] almost surely and Eτ=α (or Eτ≤α) for some α. The nondecreasing process and T are allowed to be dependent. In fact a more general setup involving σ 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.
- Clearing process
- Constrained portfolio optimization
- Minimizing a stochastic convex function
- Neyman–Pearson lemma
- Quadratic function with random coefficients
- Stochastic constrained minimization