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Siegel's Paradox
Siegel's paradox is the phenomenon that uncertainty about future prices can theoretically push rational consumers to temporarily trade away their preferred consumption goods (or currency) for non-preferred goods (or currency), as part of a plan to trade back to the preferred consumption goods after prices become clearer. For example, in some models, Americans can expect to earn more American dollars on average by investing in Euros, while Europeans can expect to earn more Euros on average by investing in American dollars. The paradox was identified by economist Jeremy Siegel in 1972. Like the related two envelopes problem, the phenomenon is sometimes labeled a paradox because an agent can seem to trade for something of equal monetary value and yet, paradoxically, seem at the same time to gain monetary value from the trade. Closer analysis shows that the "monetary value" of the trade is ambiguous but that nevertheless such trades are often favorable, depending on the scenario. Ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeremy Siegel
Jeremy James Siegel (born November 14, 1945) is an American economist who is the Russell E. Palmer Professor Emeritus of Finance at the Wharton School of the University of Pennsylvania. He appears regularly on networks including CNN, CNBC and NPR, and writes regular columns for Kiplinger's Personal Finance and Yahoo! Finance. Siegel's paradox is named after him. Early life and education Siegel was born into a Jewish family in Chicago, Illinois, and graduated from Highland Park High School. He majored in mathematics and economics as an undergraduate at Columbia University, graduating in 1967 with a Bachelor of Arts (B.A.), ''summa cum laude'', with membership in Phi Beta Kappa. He obtained a Ph.D. in economics from the Massachusetts Institute of Technology (MIT) in 1971. As a graduate student he studied under Nobel Prize winners Paul Samuelson and Robert Solow. Career Academics He taught at the University of Chicago for four years before moving to the Wharton School of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two Envelopes Problem
The two envelopes problem, also known as the exchange paradox, is a paradox in probability theory. It is of special interest in decision theory and for the Bayesian interpretation of probability theory. It is a variant of an older problem known as the necktie paradox. The problem is typically introduced by formulating a hypothetical challenge like the following example: Since the situation is symmetric, it seems obvious that there is no point in switching envelopes. On the other hand, a simple calculation using expected values suggests the opposite conclusion, that it is always beneficial to swap envelopes, since the person stands to gain twice as much money if they switch, while the only risk is halving what they currently have. Introduction Problem A person is given two indistinguishable envelopes, each of which contains a sum of money. One envelope contains twice as much as the other. The person may pick one envelope and keep whatever amount it contains. They pick one env ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paradox
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites". In logic, many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself and showed that attempts to found set theory on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fischer Black
Fischer Sheffey Black (January 11, 1938 – August 30, 1995) was an American economist, best known as one of the authors of the Black–Scholes equation. Working variously at the University of Chicago, the Massachusetts Institute of Technology, and at Goldman Sachs, Black died two years before the Nobel Memorial Prize in Economic Sciences (which is not given posthumously) was awarded to his collaborator Myron Scholes and former colleague Robert C. Merton for the Black-Scholes model and Merton's application of the model to a continuous-time framework. Black also made significant contributions to the capital asset pricing model and the theory of accounting, as well as more controversial contributions in monetary economics and the theory of business cycles. Background Fischer Sheffey Black was born on January 11, 1938. He graduated from Harvard College with a major in physics in 1959 and received a PhD in applied mathematics from Harvard University in 1964. He was initially ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jensen's Inequality
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889. Given its generality, the inequality appears in many forms depending on the context, some of which are presented below. In its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean applied after convex transformation (or equivalently, the opposite inequality for concave transformations). Jensen's inequality generalizes the statement that the secant line of a convex function lies ''above'' the graph of the function, which is Jensen's inequality for two points: the secant line consists of weighted means of the convex function (for ''t'' ∈ ,1, :t f(x_1) + (1-t) f(x_2), while the g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Efficient Market
The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted basis since market prices should only react to new information. Because the EMH is formulated in terms of risk adjustment, it only makes testable predictions when coupled with a particular model of risk. As a result, research in financial economics since at least the 1990s has focused on market anomalies, that is, deviations from specific models of risk. The idea that financial market returns are difficult to predict goes back to Bachelier, Mandelbrot, and Samuelson, but is closely associated with Eugene Fama, in part due to his influential 1970 review of the theoretical and empirical research. The EMH provides the basic logic for modern risk-based theories of asset prices, and frameworks such as consumption-based asset pricing and int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk-neutral
In economics and finance, risk neutral preferences are preferences that are neither risk averse nor risk seeking. A risk neutral party's decisions are not affected by the degree of uncertainty in a set of outcomes, so a risk neutral party is indifferent between choices with equal expected payoffs even if one choice is riskier. Theory of the firm In the context of the theory of the firm, a risk neutral firm facing risk about the market price of its product, and caring only about profit, would maximize the expected value of its profit (with respect to its choices of labor input usage, output produced, etc.). But a risk averse firm in the same environment would typically take a more cautious approach. Portfolio theory In portfolio choice,Merton, Robert. "An analytic derivation of the efficient portfolio frontier," '' Journal of Financial and Quantitative Analysis'' 7, September 1972, 1851-1872. a risk neutral investor who is able to choose any combination of an array of risky ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arbitrage
Arbitrage (, ) is the practice of taking advantage of a difference in prices in two or more marketsstriking a combination of matching deals to capitalize on the difference, the profit being the difference between the market prices at which the unit is traded. Arbitrage has the effect of causing prices of the same or very similar assets in different markets to converge. When used by academics in economics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For example, an arbitrage opportunity is present when there is the possibility to instantaneously buy something for a low price and sell it for a higher price. In principle and in academic use, an arbitrage is risk-free; in common use, as in statistical arbitrage, it may refer to ''expected'' profit, though losses may occur, and in practic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision-making Paradoxes
In psychology, decision-making (also spelled decision making and decisionmaking) is regarded as the cognitive process resulting in the selection of a belief or a course of action among several possible alternative options. It could be either rational or irrational. The decision-making process is a reasoning process based on assumptions of values, preferences and beliefs of the decision-maker. Every decision-making process produces a final choice, which may or may not prompt action. Research about decision-making is also published under the label problem solving, particularly in European psychological research. Overview Decision-making can be regarded as a problem-solving activity yielding a solution deemed to be optimal, or at least satisfactory. It is therefore a process which can be more or less rational or irrational and can be based on explicit or tacit knowledge and beliefs. Tacit knowledge is often used to fill the gaps in complex decision-making processes. Usually, both o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eponymous Paradoxes
An eponym is a noun after which or for which someone or something is, or is believed to be, named. Adjectives derived from the word ''eponym'' include ''eponymous'' and ''eponymic''. Eponyms are commonly used for time periods, places, innovations, biological nomenclature, astronomical objects, works of art and media, and tribal names. Various orthographic conventions are used for eponyms. Usage of the word The term ''eponym'' functions in multiple related ways, all based on an explicit relationship between two named things. ''Eponym'' may refer to a person or, less commonly, a place or thing for which someone or something is, or is believed to be, named. ''Eponym'' may also refer to someone or something named after, or believed to be named after, a person or, less commonly, a place or thing. A person, place, or thing named after a particular person share an eponymous relationship. In this way, Elizabeth I of England is the eponym of the Elizabethan era, but the Elizabethan e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Problems
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
