Financial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on both sides of a trade". Its concern is thus the interrelation of financial variables, such as prices, interest rates and shares, as opposed to those concerning the real economy. It has two main areas of focus: asset pricing (or "investment theory") and corporate finance; the first being the perspective of providers of capital and the second of users of capital.
The subject is concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment". It therefore centers on decision making under uncertainty in the context of the financial markets, and the resultant economic and financial models and principles, and is concerned with deriving testable or policy implications from acceptable assumptions. It is built on the foundations of microeconomics and decision theory.
Financial econometrics is the branch of financial economics that uses econometric techniques to parameterise these relationships. Mathematical finance is related in that it will derive and extend the mathematical or numerical models suggested by financial economics. Note though that the emphasis there is mathematical consistency, as opposed to compatibility with economic theory.
Financial economics is usually taught at the postgraduate level; see Master of Financial Economics. Recently, specialist undergraduate degrees are offered in the discipline.
Note that this article provides an overview and survey of the field: for derivations and more technical discussion, see the specific articles linked.
The New Palgrave Dictionary of Economics (2008, 2nd ed.) also uses the JEL codes to classify its entries in v. 8, Subject Index, including Financial Economics at pp. 863–64. The corresponding footnotes below have links to entry abstracts of The New Palgrave Online for each primary or secondary JEL category (10 or fewer per page, similar to Google searches):