Generalized functions in the qualitative study of heterogeneous populations

Natali Hritonenko, Yuri Yatsenko, Askar Boranbayev

Research output: Contribution to journalArticle

Abstract

Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics.

Original languageEnglish
JournalMathematical Population Studies
DOIs
Publication statusPublished - Jan 1 2019

Fingerprint

Economics
Population
control theory
Age Distribution
age structure
Technology
Equipment and Supplies
economics
simulation
distribution

Keywords

  • age-distributed investment
  • age-structured population models
  • capital vintage
  • generalized functions
  • Optimal control
  • technological change

ASJC Scopus subject areas

  • Demography
  • Geography, Planning and Development
  • Agricultural and Biological Sciences(all)

Cite this

Generalized functions in the qualitative study of heterogeneous populations. / Hritonenko, Natali; Yatsenko, Yuri; Boranbayev, Askar.

In: Mathematical Population Studies, 01.01.2019.

Research output: Contribution to journalArticle

@article{c873926f30b3438fb8159ecd5bd0cabb,
title = "Generalized functions in the qualitative study of heterogeneous populations",
abstract = "Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics.",
keywords = "age-distributed investment, age-structured population models, capital vintage, generalized functions, Optimal control, technological change",
author = "Natali Hritonenko and Yuri Yatsenko and Askar Boranbayev",
year = "2019",
month = "1",
day = "1",
doi = "10.1080/08898480.2018.1553395",
language = "English",
journal = "Mathematical Population Studies",
issn = "0889-8480",
publisher = "Taylor and Francis",

}

TY - JOUR

T1 - Generalized functions in the qualitative study of heterogeneous populations

AU - Hritonenko, Natali

AU - Yatsenko, Yuri

AU - Boranbayev, Askar

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics.

AB - Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics.

KW - age-distributed investment

KW - age-structured population models

KW - capital vintage

KW - generalized functions

KW - Optimal control

KW - technological change

UR - http://www.scopus.com/inward/record.url?scp=85062339665&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062339665&partnerID=8YFLogxK

U2 - 10.1080/08898480.2018.1553395

DO - 10.1080/08898480.2018.1553395

M3 - Article

AN - SCOPUS:85062339665

JO - Mathematical Population Studies

JF - Mathematical Population Studies

SN - 0889-8480

ER -