A panorama of applied mathematical problems in economics

Abstract

© 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.