Abstractly, finance is concerned with the investment and deployment of assets and liabilities over "space and time": i.e. it is about performing valuation and asset allocation today, based on risk and uncertainty of future outcomes, incorporating the time value of money (determining the present value of these future values, "discounting", requires a risk-appropriate discount rate). Since the debate to whether finance is an art or a science is still open,there have been recent efforts to organize a list of unsolved problems in finance.
Financial Economics
Financial economics is the branch of economics studying the interrelation of financial variables, such as prices, interest rates and shares, as opposed to goods and services. Financial economics concentrates on influences of real economic variables on financial ones, in contrast to pure finance. It centres on pricing and managing risk management in the financial markets, and thus produces many of the and financial models commonly employed.
The discipline essentially explores how rational investors would apply risk and return to the problem of investment. The twin assumptions of rationality and market efficiency lead to modern portfolio theory (the CAPM), and to the Black–Scholes theory for option valuation; it further studies phenomena and models where these assumptions do not hold, or are extended.
"Financial economics", also considers investment under "certainty" (Fisher separation theorem, "theory of investment value", Modigliani–Miller theorem) and hence also contributes to corporate finance theory. Financial econometrics is the branch of financial economics that uses econometric techniques to parameterize the relationships suggested.
Financial Mathematics
Financial mathematics is a field of applied mathematics, concerned with financial markets. The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory that is involved in financial mathematics. Generally, mathematical finance will derive, and extend, the mathematical or numerical models suggested by financial economics.
The field is largely focused on the modelling of derivatives, although other important subfields include insurance mathematics and quantitative portfolio problems. See Outline of finance #Mathematical tools and Outline of finance #Derivatives pricing.
In terms of practice, mathematical finance also overlaps heavily with the field of computational finance (also known as financial engineering). Arguably, these are largely synonymous, although the latter focuses on application, while the former focuses on modeling and derivation. There is also a significant overlap with financial risk management.
Experimental Finance
Experimental finance aims to establish different market settings and environments to observe experimentally and provide a lens through which science can analyze agents' behavior and the resulting characteristics of trading flows, information diffusion, and aggregation, price setting mechanisms, and returns processes. Researchers in experimental finance can study to what extent existing financial economics theory makes valid predictions and therefore prove them, and attempt to discover new principles on which such theory can be extended and be applied to future financial decisions. Research may proceed by conducting trading simulations or by establishing and studying the behavior, and the way that these people act or react, of people in artificial competitive market-like settings.
Behavioral Finance
Behavioral finance studies how the psychology of investors or managers affects financial decisions and markets when making a decision that can impact either negatively or positively on one of their areas. Behavioral finance has grown over the last few decades to become central and very important to finance.
Behavioral finance includes such topics as:
- Empirical studies that demonstrate significant deviations from classical theories.
- Models of how psychology affects and impacts trading and prices
- Forecasting based on these methods.
- Studies of experimental asset markets and the use of models to forecast experiments.
A strand of behavioral finance has been dubbed quantitative behavioral finance, which uses mathematical and statistical methodology to understand behavioral biases in conjunction with valuation.
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