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

Royi Jacobovic and Offer Kella

Stochastic Processes and their Applications, 2020, vol. 130, issue 11, 7004-7018

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 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.

Keywords: Stochastic constrained minimization; Minimizing a stochastic convex function; Quadratic function with random coefficients; Clearing process; Constrained portfolio optimization; Neyman–Pearson lemma (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2020.07.006

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