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Kelly Criterion
In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected Geometric mean, geometric growth rate. John Larry Kelly Jr., a researcher at Bell Labs, described the criterion in 1956. The practical use of the formula has been demonstrated for gambling, and the same idea was used to explain Diversification (finance), diversification in investment management., page 184f. In the 2000s, Kelly-style analysis became a part of mainstream investment theory and the claim has been made that well-known successful investors including Warren Buffett and William H. Gross, Bill Gross use Kelly methods. Also see intertemporal portfolio choice. It is also the standard replacement of Power of a test, statistical power in anytime-valid statistical tests and confidence intervals, based on E-values, e-values and e-proc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odds
In probability theory, odds provide a measure of the probability of a particular outcome. Odds are commonly used in gambling and statistics. For example for an event that is 40% probable, one could say that the odds are or When gambling, odds are often given as the ratio of the possible net profit ''to'' the possible net loss. However in many situations, you pay the possible loss ("stake" or "wager") up front and, if you win, you are paid the net win plus you also get your stake returned. So wagering 2 at , pays out , which is called When Moneyline odds are quoted as a positive number , it means that a wager pays When Moneyline odds are quoted as a negative number , it means that a wager pays Odds have a simple relationship with probability. When probability is expressed as a number between 0 and 1, the relationships between probability and odds are as follows. Note that if probability is to be expressed as a percentage these probability values should be multiplied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications is that, unlike the standard deviation, its units differ from the random variable, which is why the standard devi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if it is either entirely non-decreasing, or entirely non-increasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is termed ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\right), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithm
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , then is the logarithm of to base , written , so . As a single-variable function, the logarithm to base is the inverse of exponentiation with base . The logarithm base is called the ''decimal'' or ''common'' logarithm and is commonly used in science and engineering. The ''natural'' logarithm has the number as its base; its use is widespread in mathematics and physics because of its very simple derivative. The ''binary'' logarithm uses base and is widely used in computer science, information theory, music theory, and photography. When the base is unambiguous from the context or irrelevant it is often omitted, and the logarithm is written . Logarithms were introduced by John Napier in 1614 as a means of simplifying calculation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation. There are multiple different notations for differentiation. '' Leibniz notation'', named after Gottfried Wilhelm Leibniz, is represented as the ratio of two differentials, whereas ''prime notation'' is written by adding a prime mark. Higher order notations represent repeated differentiation, and they are usually denoted in Leib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxima And Minima
In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum, they may be defined either within a given range (the ''local'' or ''relative'' extrema) or on the entire domain (the ''global'' or ''absolute'' extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. In statistics, the corresponding concept is the sample maximum and minimum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean of numbers is the Nth root, th root of their product (mathematics), product, i.e., for a collection of numbers , the geometric mean is defined as : \sqrt[n]. When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function , :\sqrt[n] = \exp \left( \frac \right). The geometric mean of two numbers is the square root of their product, for example with numbers and the geometric mean is \textstyle \sqrt = The geometric mean o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Economist
''The Economist'' is a British newspaper published weekly in printed magazine format and daily on Electronic publishing, digital platforms. It publishes stories on topics that include economics, business, geopolitics, technology and culture. Mostly written and edited in London, it has other editorial offices in the United States and in major cities in continental Europe, Asia, and the Middle East. The newspaper has a prominent focus on data journalism and interpretive analysis over News media, original reporting, to both criticism and acclaim. Founded in 1843, ''The Economist'' was first circulated by Scottish economist James Wilson (businessman), James Wilson to muster support for abolishing the British Corn Laws (1815–1846), a system of import tariffs. Over time, the newspaper's coverage expanded further into political economy and eventually began running articles on current events, finance, commerce, and British politics. Throughout the mid-to-late 20th century, it greatl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Even Money
Even money is a wagering proposition with even odds - the bettor stands to lose or win the same amount of money. Beyond gambling Gambling (also known as betting or gaming) is the wagering of something of Value (economics), value ("the stakes") on a Event (probability theory), random event with the intent of winning something else of value, where instances of strategy (ga ..., ''even money'' can mean an event whose occurrence is about as likely to occur as not. Even money is also known as 50–50. In professional gambling, even money bets typically do not have odds that are indeed 50–50. Therefore, successful gamblers have to examine any bets they make in light of the odds really being even money. For example, in roulette, betting on red or black is an even money bet. However, the presence of the green 0 and the 00 means that statistically the bettor will lose more than 50% of the time. There are variations of the game that offer '' en prison'' on 37 number tables so if a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Margin (finance)
In finance, margin is the collateral that a holder of a financial instrument has to deposit with a counterparty (most often their broker or an exchange) to cover some or all of the credit risk the holder poses for the counterparty. This risk can arise if the holder has done any of the following: * Borrowed cash from the counterparty to buy financial instruments, * Borrowed financial instruments to sell them short, * Entered into a derivative contract. The collateral for a margin account can be the cash deposited in the account or securities provided, and represents the funds available to the account holder for further share trading. On United States futures exchanges, margins were formerly called performance bonds. Most of the exchanges today use SPAN ("Standard Portfolio Analysis of Risk") methodology, which was developed by the Chicago Mercantile Exchange in 1988, for calculating margins for options and futures. Margin account A margin account is a loan account w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leverage (finance)
In finance, leverage, also known as gearing, is any technique involving borrowing funds to buy an investment. Financial leverage is named after a lever in physics, which amplifies a small input force into a greater output force. Financial leverage uses borrowed money to augment the available capital, thus increasing the funds available for (perhaps risky) investment. If successful this may generate large amounts of profit. However, if unsuccessful, there is a risk of not being able to pay back the borrowed money. Normally, a lender will set a limit on how much risk it is prepared to take, and will set a limit on how much leverage it will permit. It would often require the acquired asset to be provided as collateral security for the loan. Leverage can arise in a number of situations. Securities like options and futures are effectively leveraged bets between parties where the principal is implicitly borrowed and lent at interest rates of very short treasury bills.Mock, E. J., R. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
