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

Royi Jacobovic, Offer Kella*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageAmerican English
Pages (from-to)7004-7018
Number of pages15
JournalStochastic Processes and their Applications
Volume130
Issue number11
DOIs
StatePublished - Nov 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

  • Clearing process
  • Constrained portfolio optimization
  • Minimizing a stochastic convex function
  • Neyman–Pearson lemma
  • Quadratic function with random coefficients
  • Stochastic constrained minimization

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