The Mathematics of Economics: The Symbolic and Statistical Language of Human Behavior under Material Constraint
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".
Deadline for manuscript submissions: 30 November 2024 | Viewed by 1850
Special Issue Editor
Special Issue Information
Dear Colleagues,
The story of economics as a discipline lies in its transformation from a narrative art to a branch of applied mathematics. This Special Issue will explore the mathematical underpinnings of economics, from optimization to game and graph theory and the emergence of machine learning and artificial intelligence.
Modern economics has oscillated between equilibrium and dynamic models. Both approaches rely on optimization through linear and nonlinear programming. Optimization unites the P and Q branches of mathematical finance, which strive for ideal portfolio design and risk-neutral pricing. Few mathematical relationships are as starkly beautiful as the primal representation of quantities paired with the dual representation of prices in models of general equilibrium. Early theories on cooperative and noncooperative games now coexist alongside enormous graphs that express mathematical relationships within economics at scale. The related disciplines of econophysics and physical economics have not only reinvigorated differential and integral calculus as economic tools, but also introduced the mathematics of fractals. Through the psychophysics of risk and uncertainty, these tools can even accommodate behavioral departures from rationality, once considered to lie beyond mathematical expression within economics.
Computational tools and the advent of data at extremes in volume, velocity, and variety have given rise to a distinct branch of mathematics within economics. Econometrics, the traditional redoubt of statistical tools within economics, can no longer be content with conventional tools for measuring risk, indexing, panel data analysis, and time-series analysis. Supervised machine learning, including deep learning through artificial neural networks, now complements linear regression. Clustering, decomposition, and manifold learning harness the power of unsupervised machine learning so that data can speak for itself without human labels or the training of models. Agent-based modeling and reinforcement learning promise insights that can be unlocked by automated agents with bounded rather than omniscient rationality.
This Special Issue invites contributions addressing any of these applications of mathematics to economics. Whether as a symbolic language or as a tool for managing and interpreting immense amounts of data, mathematics holds the key to contemporary economics.
Prof. Dr. James Ming Chen
Guest Editor
Manuscript Submission Information
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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- mathematical finance
- optimization
- operations research
- risk measures
- systemic risk
- game theory
- forecasting
- econometrics
- general equilibrium theory
- new Keynesian economics
- econophysics
- graph theory
- the economics of networks
- agent-based modeling
- computational economics
- artificial intelligence
- deep learning and neural networks
- machine learning
