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

Royi Jacobovic; Offer Kella

doi:10.1016/j.spa.2020.07.006

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

Royi Jacobovic, Offer Kella^*

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

3 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 language	American English
Pages (from-to)	7004-7018
Number of pages	15
Journal	Stochastic Processes and their Applications
Volume	130
Issue number	11
DOIs	https://doi.org/10.1016/j.spa.2020.07.006
State	Published - Nov 2020

Bibliographical note

Funding Information:
Supported by grant No. 1647/17 from the Israel Science Foundation and the Vigevani Chair in Statistics, Israel.

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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title = "Minimizing a stochastic convex function subject to stochastic constraints and some applications",

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.",

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AU - Jacobovic, Royi

AU - Kella, Offer

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AB - 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.

KW - Clearing process

KW - Constrained portfolio optimization

KW - Minimizing a stochastic convex function

KW - Neyman–Pearson lemma

KW - Quadratic function with random coefficients

KW - Stochastic constrained minimization

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DO - 10.1016/j.spa.2020.07.006

M3 - Article

AN - SCOPUS:85087904816

SN - 0304-4149

VL - 130

SP - 7004

EP - 7018

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 11

ER -

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

Abstract

Bibliographical note

Keywords

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