Financial Mathematics
Financial mathematics is a main branch of applied mathematics concerned with the financial markets. Financial mathematics is the study of financial data with the tools of mathematics, mainly statistics. Such data can be movements of securities—stocks and bonds etc.—and their relations. Another large subfield is insurance mathematics.

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 attempt to discover new principles on which such theory can be extended. Research may proceed by conducting trading simulations or by establishing and studying the behaviour 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. Behavioral finance has grown over the last few decades to become central to finance.
Behavioral finance includes such topics as:
1. Empirical studies that demonstrate significant deviations from classical theories.
2. Models of how psychology affects trading and prices
3. Forecasting based on these methods.
4. Studies of experimental asset markets and 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. Some of this endeavor has been lead by Gunduz Caginalp (Professor of Mathematics and Editor of Journal of Behavioral Finance during 2001-2004) and collaborators including Vernon Smith (2002 Nobel Laureate in Economics), David Porter, Don Balenovich, Vladimira Ilieva, Ahmet Duran, Huseyin Merdan). Studies by Jeff Madura, Ray Sturm and others have demonstrated significant behavioral effects in stocks and exchange traded funds. Among other topics, quantitative behavioral finance studies behavioral effects together with the non-classical assumption of the finiteness of assets.

Personal Finance
Questions in personal finance revolve around
• How much money will be needed by an individual (or by a family), and when?
• Where will this money come from, and how?
• How can people protect themselves against unforeseen personal events, as well as those in the external economy?
• How can family assets best be transferred across generations (bequests and inheritance)?
• How does tax policy (tax subsidies or penalties) affect personal financial decisions?
• How does credit affect an individual's financial standing?
• How can one plan for a secure financial future in an environment of economic instability?
Personal financial decisions may involve paying for education, financing durable goods such as real estate and cars, buying insurance, e.g. health and property insurance, investing and saving for retirement.
Personal financial decisions may also involve paying for a loan, or debt obligations

Corporate Finance
Managerial or corporate finance is the task of providing the funds for a corporation's activities. For small business, this is referred to as SME finance. It generally involves balancing risk and profitability, while attempting to maximize an entity's wealth and the value of its stock.
Long term funds are provided by ownership equity and long-term credit, often in the form of bonds. The balance between these forms the company's capital structure. Short-term funding or working capital is mostly provided by banks extending a line of credit.
Another business decision concerning finance is investment, or fund management. An investment is an acquisition of an asset in the hope that it will maintain or increase its value. In investment management – in choosing a portfolio – one has to decide what, how much and when to invest. To do this, a company must:
• Identify relevant objectives and constraints: institution or individual goals, time horizon, risk aversion and tax considerations;
• Identify the appropriate strategy: active v. passive – hedging strategy
• Measure the portfolio performance
Financial management is duplicate with the financial function of the Accounting profession. However, financial accounting is more concerned with the reporting of historical financial information, while the financial decision is directed toward the future of the firm.