Topics: Mathematical Economics

Mathematical economics

Mathematical economics refers to the application of mathematical methods to represent economic theories and analyze problems posed in economics. It allows formulation and derivation of key relationships in a theory with clarity, generality, rigor, and simplicity.[1] Mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could not be adequately expressed informally. Further, the language of mathematics allows economists to make clear, specific, positive claims about controversial or contentious subjects that would be impossible without mathematics.[2] Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships that clarify assumptions and implications.

Formal economic modeling began in the late 19th century with the use of differential calculus to describe and predict economic behavior. Economics became more mathematical as a discipline throughout the first half of the 20th century, but it was not until the Second World War that new techniques would allow the use of mathematical formulations in almost all of economics. This rapid systematizing of economics alarmed critics of the discipline as well as some esteemed economists. John Maynard Keynes, Robert Heilbroner, Friedrich Hayek and others have criticized the broad use of mathematical models for human behavior, arguing that some human choices are irreducible to arbitrary quantities or probabilities.


Mathematical economics
The surface of the Volatility smile is a 3-D surface whereby the current market implied volatility (Z-axis) for all options on the underlier is plotted against strike price and time to maturity (X & Y-axes).