A panorama of applied mathematical problems in economics

© 2019 by the Mathematical Association of Thailand. All rights reserved. We present a variety of issues in modern economics where applied mathematics is needed. These include economic equilibrium problem where fixed point theory for Markov operators, and for ordered sets is needed; the emergent fiel...

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Main Authors: Hung T. Nguyen, Nguyen Ngoc Thach
Format: Journal
Published: 2019
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http://cmuir.cmu.ac.th/jspui/handle/6653943832/66705
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-667052019-09-16T12:55:48Z A panorama of applied mathematical problems in economics Hung T. Nguyen Nguyen Ngoc Thach Mathematics © 2019 by the Mathematical Association of Thailand. All rights reserved. We present a variety of issues in modern economics where applied mathematics is needed. These include economic equilibrium problem where fixed point theory for Markov operators, and for ordered sets is needed; the emergent field of behavioral economics (Nobel Memorial Prize in Economics 2017) where more mathematical research is needed, for example, to capture cognitive decision- making, affecting economic data, and hence econometric modeling processes. We will focus on a promising venue, namely, quantum probability as a measure of uncertainty, since, unlike Kolmogorov probability, quantum probability, borrowed from quantum physics, is non-additive and non-commutative, thus avoiding Ellsberg’s paradox (of von Neumann’s expected utility) and capturing order effects of human judgements, respectively. Evoking the development of the framework of quantum probability as behavioral probability, as well as a quantum stochastic calculus for, say, financial econometrics, we will discuss various important mathematical research problems which can be classified as applied mathematics. 2019-09-16T12:55:48Z 2019-09-16T12:55:48Z 2019-01-01 Journal 16860209 2-s2.0-85070807568 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85070807568&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/66705
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Hung T. Nguyen
Nguyen Ngoc Thach
A panorama of applied mathematical problems in economics
description © 2019 by the Mathematical Association of Thailand. All rights reserved. We present a variety of issues in modern economics where applied mathematics is needed. These include economic equilibrium problem where fixed point theory for Markov operators, and for ordered sets is needed; the emergent field of behavioral economics (Nobel Memorial Prize in Economics 2017) where more mathematical research is needed, for example, to capture cognitive decision- making, affecting economic data, and hence econometric modeling processes. We will focus on a promising venue, namely, quantum probability as a measure of uncertainty, since, unlike Kolmogorov probability, quantum probability, borrowed from quantum physics, is non-additive and non-commutative, thus avoiding Ellsberg’s paradox (of von Neumann’s expected utility) and capturing order effects of human judgements, respectively. Evoking the development of the framework of quantum probability as behavioral probability, as well as a quantum stochastic calculus for, say, financial econometrics, we will discuss various important mathematical research problems which can be classified as applied mathematics.
format Journal
author Hung T. Nguyen
Nguyen Ngoc Thach
author_facet Hung T. Nguyen
Nguyen Ngoc Thach
author_sort Hung T. Nguyen
title A panorama of applied mathematical problems in economics
title_short A panorama of applied mathematical problems in economics
title_full A panorama of applied mathematical problems in economics
title_fullStr A panorama of applied mathematical problems in economics
title_full_unstemmed A panorama of applied mathematical problems in economics
title_sort panorama of applied mathematical problems in economics
publishDate 2019
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85070807568&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/66705
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