1.
The Wall Street Journal
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The Wall Street Journal is an American business-focused, English-language international daily newspaper based in New York City. The Journal, along with its Asian and European editions, is published six days a week by Dow Jones & Company, the newspaper is published in the broadsheet format and online. The Wall Street Journal is the largest newspaper in the United States by circulation, according to the Alliance for Audited Media, the Journal had a circulation of about 2.4 million copies as of March 2013, compared with USA Todays 1.7 million. The newspaper has won 39 Pulitzer Prizes through 2015 and derives its name from Wall Street in the heart of the Financial District of Lower Manhattan. The Journal has been printed continuously since its inception on July 8,1889, by Charles Dow, Edward Jones, the Journal also publishes the luxury news and lifestyle magazine WSJ. They were later aggregated in a daily summary called the Customers Afternoon Letter. In 1896, The Dow Jones Industrial Average was officially launched and it was the first of several indices of stock and bond prices on the New York Stock Exchange. In 1899, the Journals Review & Outlook column, which still today, appeared for the first time. Journalist Clarence Barron purchased control of the company for US$130,000 in 1902, circulation was then around 7,000, Barron and his predecessors were credited with creating an atmosphere of fearless, independent financial reporting—a novelty in the early days of business journalism. In 1921, Barrons, Americas premier financial weekly, was founded, Barron died in 1928, a year before Black Tuesday, the stock market crash that greatly affected the Great Depression in the United States. Barrons descendants, the Bancroft family, would continue to control the company until 2007, the Journal took its modern shape and prominence in the 1940s, a time of industrial expansion for the United States and its financial institutions in New York. Bernard Kilgore was named managing editor of the paper in 1941, under Kilgore, in 1947, that the paper won its first Pulitzer Prize, for William Henry Grimess editorials. In 1970, Dow Jones bought the Ottaway newspaper chain, which at the time comprised nine dailies, later, the name was changed to Dow Jones Local Media Group. In 2007 News Corp. acquired Dow Jones, a luxury lifestyle magazine, was launched in 2008. A complement to the print newspaper, The Wall Street Journal Online, was launched in 1996, in 2003, Dow Jones began to integrate reporting of the Journals print and online subscribers together in Audit Bureau of Circulations statements. In 2007, it was believed to be the largest paid-subscription news site on the Web. Since then, online subscribership has fallen, due in part to rising subscription costs, in May 2008, an annual subscription to the online edition of The Wall Street Journal cost $119 for those who do not have subscriptions to the print edition. By June 2013, the monthly cost for a subscription to the edition was $22.99, or $275.88 annually
2.
Numerical analysis
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Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. Being able to compute the sides of a triangle is important, for instance, in astronomy, carpentry. Numerical analysis continues this tradition of practical mathematical calculations. Much like the Babylonian approximation of the root of 2, modern numerical analysis does not seek exact answers. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors, before the advent of modern computers numerical methods often depended on hand interpolation in large printed tables. Since the mid 20th century, computers calculate the required functions instead and these same interpolation formulas nevertheless continue to be used as part of the software algorithms for solving differential equations. Computing the trajectory of a spacecraft requires the accurate numerical solution of a system of differential equations. Car companies can improve the safety of their vehicles by using computer simulations of car crashes. Such simulations essentially consist of solving differential equations numerically. Hedge funds use tools from all fields of analysis to attempt to calculate the value of stocks. Airlines use sophisticated optimization algorithms to decide ticket prices, airplane and crew assignments, historically, such algorithms were developed within the overlapping field of operations research. Insurance companies use programs for actuarial analysis. The rest of this section outlines several important themes of numerical analysis, the field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago, to facilitate computations by hand, large books were produced with formulas and tables of data such as interpolation points and function coefficients. The function values are no very useful when a computer is available. The mechanical calculator was developed as a tool for hand computation. These calculators evolved into electronic computers in the 1940s, and it was found that these computers were also useful for administrative purposes. But the invention of the computer also influenced the field of analysis, since now longer
3.
Financial economics
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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 and it has two main areas of focus, asset pricing 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 and it is built on the foundations of microeconomics and decision theory. Financial econometrics is the branch of 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 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. As above, the discipline essentially explores how rational investors would apply decision theory to the problem of investment, the subject is thus built on the foundations of microeconomics and decision theory, and derives several key results for the application of decision making under uncertainty to the financial markets. Underlying all of economics are the concepts of present value. Its history is correspondingly early, Richard Witt discusses compound interest already in 1613, in his book Arithmeticall Questions, further developed by Johan de Witt and these ideas originate with Blaise Pascal and Pierre de Fermat. This decision method, however, fails to consider risk aversion, choice under uncertainty here, may then be characterized as the maximization of expected utility. The impetus for these ideas arise from various inconsistencies observed under the expected value framework, the development here originally due to Daniel Bernoulli, and later formalized by John von Neumann and Oskar Morgenstern. The concepts of arbitrage-free, rational, pricing and equilibrium are then coupled with the above to derive classical financial economics, Rational pricing is the assumption that asset prices will reflect the arbitrage-free price of the asset, as any deviation from this price will be arbitraged away. This assumption is useful in pricing fixed income securities, particularly bonds, intuitively, this may be seen by considering that where an arbitrage opportunity does exist, then prices can be expected to change, and are therefore not in equilibrium. An arbitrage equilibrium is thus a precondition for a general economic equilibrium, the formal derivation will proceed by arbitrage arguments. All pricing models are then essentially variants of this, given specific assumptions and/or conditions and this approach is consistent with the above, but with the expectation based on the market as opposed to individual preferences. In general, this premium may be derived by the CAPM as will be seen under #Uncertainty, with the above relationship established, the further specialized Arrow–Debreu model may be derived. This important result suggests that, under certain conditions, there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy
4.
Logarithm
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In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed number, in simple cases the logarithm counts factors in multiplication. For example, the base 10 logarithm of 1000 is 3, the logarithm of x to base b, denoted logb, is the unique real number y such that by = x. For example, log2 =6, as 64 =26, the logarithm to base 10 is called the common logarithm and has many applications in science and engineering. The natural logarithm has the e as its base, its use is widespread in mathematics and physics. The binary logarithm uses base 2 and is used in computer science. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations and they were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the function in the 18th century. Logarithmic scales reduce wide-ranging quantities to tiny scopes, for example, the decibel is a unit quantifying signal power log-ratios and amplitude log-ratios. In chemistry, pH is a measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and they describe musical intervals, appear in formulas counting prime numbers, inform some models in psychophysics, and can aid in forensic accounting. In the same way as the logarithm reverses exponentiation, the logarithm is the inverse function of the exponential function applied to complex numbers. The discrete logarithm is another variant, it has uses in public-key cryptography, the idea of logarithms is to reverse the operation of exponentiation, that is, raising a number to a power. For example, the power of 2 is 8, because 8 is the product of three factors of 2,23 =2 ×2 ×2 =8. It follows that the logarithm of 8 with respect to base 2 is 3, the third power of some number b is the product of three factors equal to b. More generally, raising b to the power, where n is a natural number, is done by multiplying n factors equal to b. The n-th power of b is written bn, so that b n = b × b × ⋯ × b ⏟ n factors, exponentiation may be extended to by, where b is a positive number and the exponent y is any real number. For example, b−1 is the reciprocal of b, that is, the logarithm of a positive real number x with respect to base b, a positive real number not equal to 1, is the exponent by which b must be raised to yield x
5.
Normal distribution
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In probability theory, the normal distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are used in the natural and social sciences to represent real-valued random variables whose distributions are not known. The normal distribution is useful because of the limit theorem. Physical quantities that are expected to be the sum of independent processes often have distributions that are nearly normal. Moreover, many results and methods can be derived analytically in explicit form when the relevant variables are normally distributed, the normal distribution is sometimes informally called the bell curve. However, many other distributions are bell-shaped, the probability density of the normal distribution is, f =12 π σ2 e −22 σ2 Where, μ is mean or expectation of the distribution. σ is standard deviation σ2 is variance A random variable with a Gaussian distribution is said to be distributed and is called a normal deviate. The simplest case of a distribution is known as the standard normal distribution. The factor 1 /2 in the exponent ensures that the distribution has unit variance and this function is symmetric around x =0, where it attains its maximum value 1 /2 π and has inflection points at x = +1 and x = −1. Authors may differ also on which normal distribution should be called the standard one, the probability density must be scaled by 1 / σ so that the integral is still 1. If Z is a normal deviate, then X = Zσ + μ will have a normal distribution with expected value μ. Conversely, if X is a normal deviate, then Z = /σ will have a standard normal distribution. Every normal distribution is the exponential of a function, f = e a x 2 + b x + c where a is negative. In this form, the mean value μ is −b/, for the standard normal distribution, a is −1/2, b is zero, and c is − ln /2. The standard Gaussian distribution is denoted with the Greek letter ϕ. The alternative form of the Greek phi letter, φ, is used quite often. The normal distribution is often denoted by N. Thus when a random variable X is distributed normally with mean μ and variance σ2, some authors advocate using the precision τ as the parameter defining the width of the distribution, instead of the deviation σ or the variance σ2
6.
Stock
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The stock of a corporation is constituted of the equity stock of its owners. A single share of the stock represents fractional ownership of the corporation in proportion to the number of shares. In liquidation, the stock represents the residual assets of the company that would be due to stockholders after discharge of all senior claims such as secured and unsecured debt. Stockholders equity cannot be withdrawn from the company in a way that is intended to be detrimental to the companys creditors, the stock of a corporation is partitioned into shares, the total of which are stated at the time of business formation. Additional shares may subsequently be authorized by the shareholders and issued by the company. In some jurisdictions, each share of stock has a certain declared par value, in other jurisdictions, however, shares of stock may be issued without associated par value. Shares represent a fraction of ownership in a business, a business may declare different types of shares, each having distinctive ownership rules, privileges, or share values. Ownership of shares may be documented by issuance of a stock certificate. A stock certificate is a document that specifies the amount of shares owned by the shareholder. Stock typically takes the form of shares of common stock or preferred stock. As a unit of ownership, common stock typically carries voting rights that can be exercised in corporate decisions, shares of such stock are called convertible preferred shares. New equity issue may have specific legal clauses attached that differentiate them from previous issues of the issuer. Some shares of stock may be issued without the typical voting rights, for instance, or some shares may have special rights unique to them. Often, new issues that have not been registered with a governing body may be restricted from resale for certain periods of time. Preferred stock may be hybrid by having the qualities of bonds of fixed returns and they also have preference in the payment of dividends over common stock and also have been given preference at the time of liquidation over common stock. They have other features of accumulation in dividend, Rule 144 Stock is an American term given to shares of stock subject to SEC Rule 144, Selling Restricted and Control Securities. Under Rule 144, restricted and controlled securities are acquired in unregistered form, investors either purchase or take ownership of these securities through private sales from the issuing company or from an affiliate of the issuer. Investors wishing to sell these securities are subject to different rules than those selling traditional common or preferred stock and these individuals will only be allowed to liquidate their securities after meeting the specific conditions set forth by SEC Rule 144
7.
Random walk
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A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers. As illustrated by examples, random walks have applications to many scientific fields including ecology, psychology, computer science, physics, chemistry. Random walks explain the behaviors of many processes in these fields. As a more mathematical application, the value of pi can be approximated by the usage of random walk in agent-based modelling environment, the term random walk was first introduced by Karl Pearson in 1905. Various types of walks are of interest, which can differ in several ways. The time parameter can also be manipulated, in the simplest context the walk is in discrete time, that is a sequence of random variables = indexed by the natural numbers. However, it is possible to define random walks which take their steps at random times. Specific cases or limits of random walks include the Lévy flight, Random walks are a fundamental topic in discussions of Markov processes. Their mathematical study has been extensive, several properties, including dispersal distributions, first-passage or hitting times, encounter rates, recurrence or transience, have been introduced to quantify their behaviour. A popular random walk model is that of a walk on a regular lattice. In a simple walk, the location can only jump to neighboring sites of the lattice. In simple symmetric random walk on a finite lattice, the probabilities of the location jumping to each one of its immediate neighbours are the same. The best studied example is of random walk on the integer lattice Z d. An elementary example of a walk is the random walk on the integer number line, Z. This walk can be illustrated as follows, a marker is placed at zero on the number line and a fair coin is flipped. If it lands on heads, the marker is moved one unit to the right, if it lands on tails, the marker is moved one unit to the left. After five flips, the marker could now be on 1, −1,3, −3,5, with five flips, three heads and two tails, in any order, will land on 1. There are 10 ways of landing on 1,10 ways of landing on −1,5 ways of landing on 3,5 ways of landing on −3,1 way of landing on 5, see the figure below for an illustration of the possible outcomes of 5 flips
8.
Brownian motion
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Brownian motion or pedesis is the random motion of particles suspended in a fluid resulting from their collision with the fast-moving atoms or molecules in the gas or liquid. This transport phenomenon is named after the botanist Robert Brown and this explanation of Brownian motion served as convincing evidence that atoms and molecules exist, and was further verified experimentally by Jean Perrin in 1908. Perrin was awarded the Nobel Prize in Physics in 1926 for his work on the structure of matter. Brownian motion is among the simplest of the stochastic processes. This universality is closely related to the universality of the normal distribution, in both cases, it is often mathematical convenience, rather than the accuracy of the models, that motivates their use. The Roman Lucretiuss scientific poem On the Nature of Things has a description of Brownian motion of dust particles in verses 113 –140 from Book II. He uses this as a proof of the existence of atoms, Observe what happens when sunbeams are admitted into a building and you will see a multitude of tiny particles mingling in a multitude of ways. Their dancing is an indication of underlying movements of matter that are hidden from our sight. It originates with the atoms which move of themselves, then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible. Although the mingling motion of dust particles is caused largely by air currents, while Jan Ingenhousz described the irregular motion of coal dust particles on the surface of alcohol in 1785, the discovery of this phenomenon is often credited to the botanist Robert Brown in 1827. Brown was studying pollen grains of the plant Clarkia pulchella suspended in water under a microscope when he observed minute particles, ejected by the pollen grains, executing a jittery motion. By repeating the experiment with particles of matter he was able to rule out that the motion was life-related. The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in a paper on the method of least squares published in 1880. This was followed independently by Louis Bachelier in 1900 in his PhD thesis The theory of speculation, in which he presented an analysis of the stock. The Brownian motion model of the market is often cited. Albert Einstein and Marian Smoluchowski brought the solution of the problem to the attention of physicists and their equations describing Brownian motion were subsequently verified by the experimental work of Jean Baptiste Perrin in 1908. In this way Einstein was able to determine the size of atoms, in accordance to Avogadros law this volume is the same for all ideal gases, which is 22.414 liters at standard temperature and pressure
9.
Supply and demand
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In microeconomics, supply and demand is an economic model of price determination in a market. By contrast, responses to changes in the price of the good are represented as movements along unchanged supply, a supply schedule is a table that shows the relationship between the price of a good and the quantity supplied. Under the assumption of perfect competition, supply is determined by marginal cost and that is, firms will produce additional output while the cost of producing an extra unit of output is less than the price they would receive. A hike in the cost of raw goods would decrease supply, shifting costs up, while a discount would increase supply, shifting costs down, by its very nature, conceptualizing a supply curve requires the firm to be a perfect competitor. This is true because each point on the curve is the answer to the question If this firm is faced with this potential price, how much output will it be able to. Economists distinguish between the curve of an individual firm and between the market supply curve. The market supply curve is obtained by summing the quantities supplied by all suppliers at each potential price, thus, in the graph of the supply curve, individual firms supply curves are added horizontally to obtain the market supply curve. Economists also distinguish the market supply curve from the long-run market supply curve. In this context, two things are assumed constant by definition of the run, the availability of one or more fixed inputs. In the long run, firms have a chance to adjust their holdings of physical capital, furthermore, in the long run potential competitors can enter or exit the industry in response to market conditions. For both of these reasons, long-run market supply curves are generally flatter than their short-run counterparts, the determinants of supply are, Production costs, how much a goods costs to be produced. Production costs are the cost of the inputs, primarily labor, capital, energy and they depend on the technology used in production, and/or technological advances. Following the law of demand, the curve is almost always represented as downward-sloping, meaning that as price decreases. Just like the supply curves reflect marginal cost curves, demand curves are determined by marginal utility curves, the demand schedule is defined as the willingness and ability of a consumer to purchase a given product in a given frame of time. It is aforementioned, that the curve is generally downward-sloping. Two different hypothetical types of goods with upward-sloping demand curves are Giffen goods, by its very nature, conceptualizing a demand curve requires that the purchaser be a perfect competitor—that is, that the purchaser has no influence over the market price. This is true because each point on the curve is the answer to the question If this buyer is faced with this potential price. If a buyer has market power, so its decision of how much to buy influences the price, then the buyer is not faced with any price
10.
Derivative (finance)
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In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter or on a such as the Bombay Stock Exchange. Derivatives are one of the three categories of financial instruments, the other two being stocks and debt. More recent historical origin is Bucket shop that were outlawed a century ago, Derivatives are contracts between two parties that specify conditions under which payments are to be made between the parties. The assets include commodities, stocks, bonds, interest rates and currencies, but they can also be other derivatives, from the economic point of view, financial derivatives are cash flows, that are conditioned stochastically and discounted to present value. The market risk inherent in the asset is attached to the financial derivative through contractual agreements. The underlying asset does not have to be acquired, Derivatives therefore allow the breakup of ownership and participation in the market value of an asset. This also provides an amount of freedom regarding the contract design. That contractual freedom allows to modify the participation in the performance of the underlying asset almost arbitrarily, thus, the participation in the market value of the underlying can be effectively weaker, stronger, or implemented as inverse. Hence, specifically the price risk of the underlying asset can be controlled in almost every situation. Derivatives are more common in the era, but their origins trace back several centuries. One of the oldest derivatives is rice futures, which have traded on the Dojima Rice Exchange since the eighteenth century. Derivatives are broadly categorized by the relationship between the asset and the derivative, the type of underlying asset, the market in which they trade. Derivatives may broadly be categorized as lock or option products, lock products obligate the contractual parties to the terms over the life of the contract. Option products provide the buyer the right, but not the obligation to enter the contract under the terms specified, Derivatives can be used either for risk management or for speculation. Along with many financial products and services, derivatives reform is an element of the Dodd–Frank Wall Street Reform. The Act delegated many rule-making details of regulatory oversight to the Commodity Futures Trading Commission, however, these are notional values, and some economists say that this value greatly exaggerates the market value and the true credit risk faced by the parties involved
11.
Market liquidity
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In business, economics or investment, market liquidity is a markets ability to purchase or sell an asset without causing drastic change in the assets price. Equivalently, a market liquidity describes the assets ability to sell quickly without having to reduce its price to a significant degree. Liquidity is about how big the trade-off is between the speed of the sale and the price it can be sold for, in a liquid market, the trade-off is mild, selling quickly will not reduce the price much. In a relatively illiquid market, selling it quickly will require cutting its price by some amount, money, or cash, is the most liquid asset, because it can be sold for goods and services instantly with no loss of value. There is no wait for a buyer of the cash. There is no trade-off between speed and value and it can be used immediately to perform economic actions like buying, selling, or paying debt, meeting immediate wants and needs. If an asset is moderately liquid, it has moderate liquidity, in an alternative definition, liquidity can mean the amount of cash and cash equivalents. If a business has moderate liquidity, it has an amount of very liquid assets. If a business has sufficient liquidity, it has a sufficient amount of liquid assets. An act of exchanging a less liquid asset for a liquid asset is called liquidation. Often liquidation is trading the less liquid asset for cash, also known as selling it, for the same asset, its liquidity can change through time or between different markets, such as in different countries. The change in the liquidity is just based on the market liquidity for the asset at the particular time or in the particular country. The liquidity of a product can be measured as how often it is bought, Liquidity is defined formally in many accounting regimes and has in recent years been more strictly defined. For instance, the US Federal Reserve intends to apply quantitative liquidity requirements based on Basel III liquidity rules as of fiscal 2012, bank directors will also be required to know of, and approve, major liquidity risks personally. A liquid asset has some or all of the features, It can be sold rapidly, with minimal loss of value. The essential characteristic of a market is that there are always ready. A market may be considered both deep and liquid if there are ready and willing buyers and sellers in large quantities, an illiquid asset is an asset which is not readily salable due to uncertainty about its value or the lack of a market in which it is regularly traded. The mortgage-related assets which resulted in the mortgage crisis are examples of illiquid assets