Finance refers to monetary resources and to the study anddiscipline ofmoney,currency,assets andliabilities.^[a] As a subject of study, it is related to but distinct fromeconomics, which is the study of theproduction,distribution, andconsumption ofgoods and services.^[b] Based on the scope of financial activities infinancial systems, the discipline can be divided intopersonal,corporate, andpublic finance.

In these financial systems, assets are bought, sold, or traded asfinancial instruments, such ascurrencies,loans,bonds,shares,stocks,options,futures, etc. Assets can also bebanked,invested, andinsured to maximize value and minimize loss. In practice,risks are always present in any financial action and entities.

Due to its wide scope, a broad range of subfields exists within finance.Asset-,money-,risk- andinvestment management aim to maximize value and minimizevolatility.Financial analysis assesses the viability, stability, and profitability of an action or entity. Some fields are multidisciplinary, such asmathematical finance,financial law,financial economics,financial engineering andfinancial technology. These fields are the foundation ofbusiness andaccounting. In some cases,theories in finance can be tested using thescientific method, covered byexperimental finance.

The early history of finance parallels the earlyhistory of money, which isprehistoric. Ancient and medieval civilizations incorporated basic functions of finance, such as banking, trading and accounting, into their economies. In the late 19th century, theglobal financial system was formed.

In the middle of the 20th century, finance emerged as a distinct academic discipline,^[c] separate from economics.^[1] The earliest doctoral programs in finance were established in the 1960s and 1970s.^[2] Today, finance is alsowidely studied throughcareer-focused undergraduate andmaster's level programs.^[3][4]

As outlined, the financial system consists of the flows of capital that take place between individuals and households (personal finance), governments (public finance), and businesses (corporate finance). "Finance" thus studies the process of channeling money from savers and investors to entities that need it.^[d] Savers and investors have money available which could earn interest or dividends if put to productive use. Individuals, companies and governments must obtain money from some external source, such as loans or credit, when they lack sufficient funds to run their operations.

In general, an entity whose income exceeds itsexpenditure can lend or invest the excess, intending to earn a fair return. Correspondingly, an entity where income is less than expenditure can raise capital usually in one of two ways: (i) by borrowing in the form of a loan (private individuals), or by sellinggovernment or corporate bonds; (ii) by a corporation sellingequity, also called stock or shares (which may take various forms:preferred stock orcommon stock). The owners of both bonds and stock may beinstitutional investors—financial institutions such as investment banks andpension funds—or private individuals, calledprivate investors orretail investors. (SeeFinancial market participants.)

Thelending is often indirect, through afinancial intermediary such as abank, or via the purchase of notes orbonds (corporate bonds,government bonds, or mutual bonds) in thebond market. The lender receives interest, theborrower pays a higher interest than the lender receives, and the financial intermediary earns the difference for arranging the loan.^[6][7][8]A bank aggregates the activities of many borrowers and lenders. Banks accept deposits from individuals and businesses, paying interest on these funds. The bank then lends these deposits to borrowers. Banks facilitate transactions between borrowers and lenders of various sizes, enabling efficient financial coordination.

Investing typically entails the purchase ofstock, either individual securities or via amutual fund, for example. Stocks are usually sold by corporations to investors so as to raise required capital in the form of "equity financing", as distinct from thedebt financing described above. The financial intermediaries here are theinvestment banks. The investment banksfind the initial investors and facilitate the listing of the securities, typically shares and bonds. Additionally, they facilitate thesecurities exchanges, which allow their trade thereafter, as well as the various service providers which manage the performance or risk of these investments. These latter includemutual funds,pension funds,wealth managers, andstock brokers, typically servicingretail investors (private individuals).

Inter-institutional trade and investment, andfund-management at this scale, is referred to as "wholesale finance". Institutions hereextend the products offered, with related trading, to include bespokeoptions,swaps, andstructured products, as well asspecialized financing; this "financial engineering" isinherently mathematical, and these institutions are then the major employers of"quants" (seebelow). In these institutions,risk management,regulatory capital, andcompliance play major roles.

As outlined, finance comprises, broadly, the three areas of personal finance, corporate finance, and public finance. These, in turn, overlap and employ various activities and sub-disciplines—chieflyinvestments, risk management, andquantitative finance.

Personal finance refers to the practice of budgeting to ensure enough funds are available to meet basic needs, while ensuring there is only a reasonable level of risk to lose said capital. Personal finance may involve paying for education, financingdurable goods such asreal estate and cars, buyinginsurance, investing, and saving forretirement.^[9] Personal finance may also involve paying for a loan or other debt obligations. The main areas of personal finance are considered to be income, spending, saving, investing, and protection. The following steps, as outlined by the Financial Planning Standards Board,^[10] suggest that an individual will understand a potentially secure personal finance plan after:

• Purchasing insurance to ensure protection against unforeseen personal events;
• Understanding the effects of tax policies, subsidies, or penalties on the management of personal finances;
• Understanding the effects of credit on individual financial standing;
• Developing a savings plan or financing for large purchases (auto, education, home);
• Planning a secure financial future in an environment of economic instability;
• Pursuing a checking or a savings account;
• Preparing for retirement or other long term expenses.^[11]

Corporate finance deals with the actions that managers take to increase the value of the firm to the shareholders, the sources of funding and thecapital structure of corporations, and the tools and analysis used to allocate financial resources. While corporate finance is in principle different frommanagerial finance, which studies thefinancial management of all firms rather than corporations alone, the concepts are applicable to the financial problems of all firms,^[12] and this area is then often referred to as "business finance".

Typically, "corporate finance" relates to thelong term objective of maximizing the value of theentity's assets, itsstock, and itsreturn to shareholders, while alsobalancing risk and profitability. This entails^[13] three primary areas:

1. Capital budgeting: selecting which projects to invest in—here, accuratelydetermining value is crucial, as judgements about asset values can be "make or break".^[14]
2. Dividend policy: the use of "excess" funds—these are to be reinvested in the business or returned to shareholders.
3. Capital structure: deciding on the mix of funding to be used—here attempting to find theoptimal capital mix re debt-commitments vscost of capital.

The lattercreates the link withinvestment banking andsecurities trading, as above, in that the capital raised will generically comprise debt, i.e.corporate bonds, andequity, oftenlisted shares. Re risk management within corporates, seebelow.

Financial managers—i.e. as distinct from corporate financiers—focus more on theshort term elements of profitability, cash flow, and "working capital management" (inventory, credit anddebtors), ensuring that the firm cansafely and profitably carry out its financialand operational objectives; i.e. that it: (1) can service both maturing short-term debt repayments, and scheduled long-term debt payments, and (2) has sufficient cash flow for ongoing and upcomingoperational expenses. (SeeFinancial management andFP&A.)

Public finance describes finance as related to sovereign states, sub-national entities, and related public entities or agencies. It generally encompasses a long-term strategic perspective regarding investment decisions that affect public entities.^[15] These long-term strategic periods typically encompass five or more years.^[16] Public finance is primarily concerned with:^[17]

• Identification ofrequired expenditures of a public sector entity;
• Source(s) of thatentity's revenue;
• Thebudgeting process;
• Sovereigndebt issuance, ormunicipal bonds forpublic works projects.

Central banks, such as theFederal Reserve System banks in theUnited States and theBank of England in theUnited Kingdom, are strong players in public finance. They act aslenders of last resort as well as strong influences on monetary and credit conditions in the economy.^[18]

Development finance, which is related, concerns investment ineconomic development projects provided by a(quasi) governmental institution on a non-commercial basis; these projects would otherwise not be ableto get financing. Apublic–private partnership is primarily used forinfrastructure projects: a private sector corporate provides the financing up-front, and then draws profits from taxpayers or users.Climate finance, and the relatedEnvironmental finance, address the financial strategies, resourcesand instruments used inclimate change mitigation.

Investment management^[12] is the professional asset management of various securities—typically shares and bonds, but also other assets, such as real estate, commodities andalternative investments—in order to meet specified investment goals for the benefit of investors.

As above, investors may be institutions, such as insurance companies, pension funds, corporations, charities, educational establishments, or private investors, either directly via investment contracts or, more commonly, via collective investment schemes like mutual funds,exchange-traded funds, orreal estate investment trusts.

At the heart of investment management^[12] isasset allocation—diversifying the exposure among theseasset classes, and among individual securities within each asset class—as appropriate to the client'sinvestment policy, in turn, a function of risk profile, investment goals, and investment horizon (seeInvestor profile). Here:

• Portfolio optimization is the process of selecting the best portfolio given the client's objectives and constraints.
• Fundamental analysis is the approach typically applied invaluing and evaluating the individual securities.
• Technical analysis is about forecasting future asset prices with past data.^[19]

Overlaid is the portfolio manager'sinvestment style—broadly,active vspassive,value vsgrowth, andsmall cap vs.large cap—andinvestment strategy.

In a well-diversified portfolio, achievedinvestment performance will, in general, largely be a function of the asset mix selected, while the individual securities are less impactful. The specific approach or philosophy will also be significant, depending on the extent to which it is complementary with themarket cycle.

Additional to thisdiversification, the fundamental risk mitigant employed,investment managers will apply various hedging techniques as appropriate,^[12] these may relate to theportfolio as a whole orto individual stocks.Bond portfolios are often (instead) managed viacash flow matching orimmunization, while for derivative portfolios and positions, traders use"the Greeks" to measure and then offset sensitivities. In parallel, managers –active andpassive –will monitortracking error, thereby minimizing and preempting any underperformancevs their "benchmark".

Aquantitative fund is managed usingcomputer-based mathematical techniques (increasingly,machine learning) instead of human judgment. The actual tradingis typically automated viasophisticated algorithms.

Risk management, in general, is the study of how to control risks and balance the possibility of gains; it is the process of measuring risk and then developing and implementing strategies to manage that risk.Financial risk management^[20][21] is the practice of protectingcorporate value againstfinancial risks, often by"hedging" exposure to these using financial instruments. The focus is particularly on credit and market risk, and in banks, through regulatory capital, includes operational risk.

• Credit risk is the risk ofdefault on a debt that may arise from a borrower failing to make required payments;
• Market risk relates to losses arising from movements in market variables such as prices and exchange rates;
• Operational risk relates to failures in internal processes, people, and systems, or to external events (these risks will often beinsured).

Financial risk management isrelated to corporate finance^[12] in two ways. Firstly, firm exposure to market risk is a direct result of previous capital investments and funding decisions; while credit risk arises from the business's credit policy and is often addressed throughcredit insurance andprovisioning. Secondly, both disciplines share the goal of enhancing or at least preserving, the firm'seconomic value, and in this context^[22] overlaps alsoenterprise risk management, typically the domain ofstrategic management. Here, businesses devote much time and effort toforecasting,analytics andperformance monitoring. (SeeALM andtreasury management.)

For banks and other wholesale institutions,^[23] risk managementfocuses on managing, and as necessary hedging, the various positions held by the institution—bothtrading positions andlong term exposures—and on calculating and monitoring the resultanteconomic capital, andregulatory capital underBasel III. The calculations here are mathematically sophisticated, and within the domain ofquantitative finance as below. Credit risk is inherent in the business of banking, but additionally, these institutions are exposed tocounterparty credit risk. Banks typically employMiddle office"Risk Groups", whereasfront office risk teams provide risk "services" (or "solutions") to customers.

Insurers^[24]manage their own risks with a focus onsolvency and the ability to pay claims:Life Insurers are concerned more withlongevity risk andinterest rate risk; Short-Term Insurers (Property,Health,Casualty) emphasizecatastrophe- and claims volatility risks. For expected claimsreserves are set aside periodically, while to absorb unexpected losses, a minimumlevel of capital is maintained.

Quantitative finance—also referred to as "mathematical finance"—includes those finance activities wherea sophisticated mathematical model is required,^[25] and thus overlaps several of the above.

As a specialized practice area, quantitative finance comprises primarily three sub-disciplines; the underlying theory and techniquesare discussed in the next section:

1. Quantitative finance is often synonymous withfinancial engineering. This area generally underpins a bank'scustomer-driven derivatives business—delivering bespokeOTC-contracts and"exotics", anddesigning the various structured products and solutions mentioned—and encompassesmodeling and programming in support of the initial trade, and its subsequent hedging and management.
2. Quantitative finance also significantly overlapsfinancial risk management in banking, asmentioned, both as regards this hedging, and as regards economic capital as well as compliance with regulations andthe Basel capital / liquidity requirements.
3. "Quants" are also responsible for building and deploying the investment strategies at the quantitative fundsmentioned; they are also involved inquantitative investing more generally, in areas such astrading strategy formulation, and inautomated trading,high-frequency trading,algorithmic trading, andprogram trading.

Financial theory is studied and developed within the disciplines ofmanagement,(financial)economics,accountancy andapplied mathematics.In the abstract,^[12][26]finance is concerned with the investment and deployment ofassets andliabilities over "space and time"; i.e., it is about performingvaluation andasset allocation today, based on the risk and uncertainty of future outcomes while appropriately incorporating thetime value of money. Determining thepresent value of these future values, "discounting", must be at therisk-appropriate discount rate, in turn, a major focus of finance-theory.^[27]As financial theory has roots in many disciplines, including mathematics, statistics, economics, physics, and psychology, it can be considered a mix of anart andscience,^[1] and there are ongoing related efforts to organize alist of unsolved problems in finance.

Managerial finance^[29] is the branch of finance that deals with the financial aspects of themanagement of a company, and the financial dimension of managerial decision-making more broadly. It provides thetheoretical underpin for the practicedescribed above, concerning itself with themanagerial application of the variousfinance techniques. Academics working in this area are typically based inbusiness school finance departments, inaccounting, or inmanagement science.

The tools addressed and developed relate in the main tomanagerial accounting andcorporate finance: the former allow management to better understand, and hence act on, financial information relating toprofitability and performance; the latter, as above, are about optimizing the overall financial structure, including its impact on working capital. Key aspects of managerial finance thus include:

1. Financial planning and forecasting
2. Capital budgeting
3. Capital structure
4. Working capital management
5. Risk management
6. Financial analysis and reporting.

The discussion, however, extends tobusiness strategy more broadly, emphasizing alignment with the company's overall strategic objectives; and similarly incorporates themanagerial perspectives of planning, directing, and controlling.

Financial economics^[31] is the branch ofeconomics that studies the interrelation of financialvariables, such asprices,interest rates and shares, as opposed toreal economic variables, i.e.goods and services. It thus centers on pricing, decision making, and risk management in thefinancial markets,^[31][26] and produces many of the commonly employedfinancial models. (Financial econometrics is the branch of financial economics that uses econometric techniques to parameterize the relationships suggested.)

The discipline has two main areas of focus:^[26]asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital; respectively:

1. Asset pricing theory develops the models used in determining the risk-appropriate discount rate, and in pricing derivatives; and includes theportfolio- andinvestment theory applied in asset management. The analysis essentially explores howrational investors would apply risk and return to the problem ofinvestment under uncertainty, producing the key "Fundamental theorem of asset pricing". Here, the twin assumptions ofrationality andmarket efficiency lead tomodern portfolio theory (theCAPM), and to theBlack–Scholes theory foroption valuation. At more advanced levels—and often in response tofinancial crises—the studythen extends these"neoclassical" models to incorporate phenomena where their assumptions do not hold, or to more general settings.
2. Much ofcorporate finance theory, by contrast, considers investment under "certainty" (Fisher separation theorem,"theory of investment value", andModigliani–Miller theorem). Here, theory and methods are developed for the decisioning about funding, dividends, and capital structure discussed above. A recent development isto incorporate uncertainty andcontingency—and thus various elements of asset pricing—into these decisions, employing for examplereal options analysis.

Financial mathematics^[33] is the field ofapplied mathematics concerned withfinancial markets;Louis Bachelier's doctoral thesis, defended in 1900, is considered to be the first scholarly work in this area. The field is largely focused on themodeling of derivatives—with much emphasis oninterest rate- andcredit risk modeling—while other important areas includeinsurance mathematics andquantitative portfolio management. Relatedly, the techniques developedare applied to pricing and hedging a wide range ofasset-backed,government, andcorporate-securities.

Asabove, in terms of practice, the field is referred to as quantitative finance and / or mathematical finance, and comprises primarily the three areas discussed.Themain mathematical tools and techniques are, correspondingly:

• for derivatives,^[34]Itô's stochastic calculus,simulation, andpartial differential equations; see aside boxed discussion re the prototypicalBlack-Scholes model andthe various numeric techniques now applied
• for risk management,^[23]value at risk,stress testing and"sensitivities" analysis (applying the "greeks"); the underlying mathematics comprisesmixture models,PCA,volatility clustering andcopulas.^[35]
• in both of these areas, and particularly for portfolio problems, quants employsophisticated optimization techniques

Mathematically, these separate intotwo analytic branches: derivatives pricing usesrisk-neutral probability (orarbitrage-pricing probability), denoted by "Q"; while risk and portfolio management generally use physical (or actual or actuarial) probability, denoted by "P". These are interrelated through the above "Fundamental theorem of asset pricing".

The subject has a close relationship with financial economics, which, as outlined, is concerned with much of the underlying theory that is involved in financial mathematics: generally, financial mathematics will derive and extend themathematical models suggested.Computational finance is the branch of (applied)computer science that deals with problems of practical interest in finance, and especially^[33] emphasizes thenumerical methods applied here.

Experimental finance^[36] aims to establish different market settings and environments to experimentally observe 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, as well as 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 of people in artificial, competitive, market-like settings.

Behavioral finance studies how thepsychology of investors or managers affects financial decisions and markets^[37] and is relevant when making a decision that can impact either negatively or positively on one of their areas. With more in-depth research into behavioral finance, it is possible to bridge what actually happens in financial markets with analysis based on financial theory.^[38] Behavioral finance has grown over the last few decades to become an integral aspect of finance.^[39]

Behavioral finance includes such topics as:

1. Empirical studies that demonstrate significant deviations from classical theories;
2. Models of how psychology affects and impacts trading and prices;
3. Forecasting based on these methods;
4. Studies of experimental asset markets and the use of models to forecast experiments.

A strand of behavioral finance has been dubbedquantitative behavioral finance, which uses mathematical and statistical methodology to understand behavioral biases in conjunction with valuation.

Quantum finance involves applying quantum mechanical approaches to financial theory, providing novel methods and perspectives in the field.^[40]Quantumfinance is an interdisciplinary field, in which theories and methods developed byquantum physicists and economists are applied to solve financial problems. It represents a branch known as econophysics. Althoughquantum computational methods have been around for quite some time and use the basic principles of physics to better understand the ways to implement and manage cash flows, it is mathematics that is actually important in this new scenario^[41] Finance theory is heavily based on financial instrument pricing such asstock option pricing. Many of the problems facing the finance community have no known analytical solution. As a result, numerical methods and computer simulations for solving these problems have proliferated. This research area is known ascomputational finance. Many computational finance problems have a high degree of computational complexity and are slow to converge to a solution on classical computers. In particular, when it comes to option pricing, there is additional complexity resulting from the need to respond to quickly changing markets. For example, in order to take advantage of inaccurately priced stock options, the computation must complete before the next change in the almost continuously changing stock market. As a result, the finance community is always looking for ways to overcome the resulting performance issues that arise when pricing options. This has led to research that applies alternative computing techniques to finance. Most commonly used quantum financial models are quantum continuous model, quantum binomial model, multi-step quantum binomial model etc.

The origin of finance can be traced to the beginning of state formation and trade during theBronze Age. The earliest historical evidence of finance is dated to around 3000 BCE. Banking originated in West Asia, where temples and palaces were used as safe places for the storage of valuables. Initially, the only valuable that could be deposited was grain, but cattle and precious materials were eventually included. During the same period, the Sumerian city ofUruk inMesopotamia supported trade by lending as well as the use of interest. In Sumerian, "interest" wasmas, which translates to "calf". In Greece and Egypt, the words used for interest,tokos andms respectively, meant "to give birth". In these cultures, interest indicated a valuable increase, and seemed to consider it from the lender's point of view.^[42] TheCode of Hammurabi (1792–1750 BCE) included laws governing banking operations. The Babylonians were accustomed to charging interest at the rate of 20 percent per year. By 1200 BCE,cowrie shells were used as a form of money inChina.

The use of coins as a means of representing money began in the years between 700 and 500 BCE.^[43] Herodotus mentions the use of crude coins inLydia around 687 BCE and, by 640 BCE, the Lydians had started to use coin money more widely and opened permanent retail shops.^[44] Shortly after, cities inClassical Greece, such asAegina,Athens, andCorinth, started minting their own coins between 595 and 570 BCE. During theRoman Republic, interest was outlawed by theLex Genucia reforms in 342 BCE, though the provision went largely unenforced. UnderJulius Caesar, a ceiling on interest rates of 12% was set, and much later underJustinian it was lowered even further to between 4% and 8%.^[45]

The first stock exchange was opened inAntwerp in 1531.^[46] Since then, popular exchanges such as theLondon Stock Exchange (founded in 1773) and theNew York Stock Exchange (founded in 1793) were created.^[47][48]

• 2007–2008 financial crisis
• Outline of finance

• Graham, Benjamin;Jason Zweig (8 July 2003) [1949].The Intelligent Investor. Warren E. Buffett (collaborator) (2003 ed.).HarperCollins. front cover.ISBN 0-06-055566-1.
• Graham, Benjamin;Dodd, David LeFevre (1934).Security Analysis: The Classic 1934 Edition.McGraw-Hill Education.ISBN 978-0-070-24496-2.LCCN 34023635.
• Bogle, John Bogle (2007).The Little Book of Common Sense Investing: The Only Way to Guarantee Your Fair Share of Stock Market Returns. John Wiley and Sons. pp. 216.ISBN 9780470102107.
• Buffett, W.; Cunningham, L.A. (2009).The Essays of Warren Buffett: Lessons for Investors and Managers.John Wiley & Sons (Asia) Pte Limited.ISBN 978-0-470-82441-2.
• Kiyosaki, Robert andSharon Lechter (2000).Rich Dad Poor Dad: What the Rich Teach Their Kids About Money That the Poor and Middle Class Do Not!Warner Business Books.ISBN 0-446-67745-0
• Stanley, Thomas J.; Danko, W.D. (1998).The Millionaire Next Door.Gallery Books.ISBN 978-0-671-01520-6.LCCN 98046515.
• Soros, George (1988).The Alchemy of Finance: Reading the Mind of the Market. A Touchstone book.Simon & Schuster.ISBN 978-0-671-66238-7.LCCN 87004745.
• Fisher, Philip Arthur (1996).Common Stocks and Uncommon Profits and Other Writings. Wiley Investment Classics.Wiley.ISBN 978-0-471-11927-2.LCCN 95051449.

• Hypertextual Finance Glossary (Campbell Harvey)
• Finance Glossary (Pierre Vernimmen)
• Glossary of financial risk management terms (Risk.net)
• Glossary of Key Investment Terms (PIMCO)
• Corporate finance resources (Aswath Damodaran)
• Financial management resources (James Van Horne)
• Personal finance resources (Financial Literacy and Education Commission, mymoney.gov)
• Public finance resources (Governance and Social Development Resource Centre, gsdrc.org) [Archived 2023-06-02 at theWayback Machine]
• Risk management resources (Global Risk Institute)