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First-order Stochastic Dominance
Stochastic dominance is a partial order between random variables. It is a form of stochastic ordering. The concept arises in decision theory and decision analysis in situations where one gamble (a probability distribution over possible outcomes, also known as prospects) can be ranked as superior to another gamble for a broad class of decision-makers. It is based on shared preferences regarding sets of possible outcomes and their associated probabilities. Only limited knowledge of preferences is required for determining dominance. Risk aversion is a factor only in second order stochastic dominance. Stochastic dominance does not give a total order, but rather only a partial order: for some pairs of gambles, neither one stochastically dominates the other, since different members of the broad class of decision-makers will differ regarding which gamble is preferable without them generally being considered to be equally attractive. Throughout the article, \rho, \nu stand for probabilit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partially Ordered Set
In mathematics, especially order theory, a partial order on a Set (mathematics), set is an arrangement such that, for certain pairs of elements, one precedes the other. The word ''partial'' is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other. Partial orders thus generalize total orders, in which every pair is comparable. Formally, a partial order is a homogeneous binary relation that is Reflexive relation, reflexive, antisymmetric relation, antisymmetric, and Transitive relation, transitive. A partially ordered set (poset for short) is an ordered pair P=(X,\leq) consisting of a set X (called the ''ground set'' of P) and a partial order \leq on X. When the meaning is clear from context and there is no ambiguity about the partial order, the set X itself is sometimes called a poset. Partial order relations The term ''partial order'' usually refers to the reflexive partial order relatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
If And Only If
In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, ''P if and only if Q'' means that ''P'' is true whenever ''Q'' is true, and the only case in which ''P'' is true is if ''Q'' is also true, whereas in the case of ''P if Q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Operations Research
''Mathematics of Operations Research'' is a quarterly peer-reviewed scientific journal established in February 1976. It focuses on areas of mathematics relevant to the field of operations research such as continuous optimization, discrete optimization, game theory, machine learning, simulation methodology, and stochastic models. The journal is published by INFORMS (Institute for Operations Research and the Management Sciences). the journal has a 2017 impact factor of 1.078. History The journal was established in 1976. The founding editor-in-chief was Arthur F. Veinott Jr. (Stanford University). He served until 1980, when the position was taken over by Stephen M. Robinson, who held the position until 1986. Erhan Cinlar served from 1987 to 1992, and was followed by Jan Karel Lenstra (1993-1998). Next was Gérard Cornuéjols (1999-2003) and Nimrod Megiddo (2004-2009). Finally came Uri Rothblum (2009-2012), Jim Dai (2012-2018), and the current editor-in-chief Katya Scheinberg (20 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk Premium
A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky Rate of return, return less the Risk-free interest rate, risk-free return, as demonstrated by the formula below. Risk \ premium = E(r) - r_f Where E(r) is the risky expected rate of return and r_f is the risk-free return. The inputs for each of these variables and the ultimate interpretation of the risk premium value differs depending on the application as explained in the following sections. Regardless of the application, the market premium can be volatile as both comprising variables can be impacted independent of each other by both cyclical and abrupt changes. This means that the market premium is dynamic in nature and ever-changing. Additionally, a general observation regardless of application is that the risk premium is larger during economic do ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skewness
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution (a distribution with a single peak), negative skew commonly indicates that the ''tail'' is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value in skewness means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat. Thus, the judgement on the symmetry of a given distribution by using only its skewness is risky; the distribution shape must be taken into account. Introduction Consider the two d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean-preserving Spread
In probability and statistics, a mean-preserving spread (MPS) is a change from one probability distribution A to another probability distribution B, where B is formed by spreading out one or more portions of A's probability density function or probability mass function while leaving the mean (the expected value) unchanged. As such, the concept of mean-preserving spreads provides a stochastic ordering of equal-mean gambles (probability distributions) according to their degree of risk; this ordering is partial, meaning that of two equal-mean gambles, it is not necessarily true that either is a mean-preserving spread of the other. Distribution A is said to be a mean-preserving contraction of B if B is a mean-preserving spread of A. Ranking gambles by mean-preserving spreads is a special case of ranking gambles by second-order stochastic dominance – namely, the special case of equal means: If B is a mean-preserving spread of A, then A is second-order stochastically dominant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concave Function
In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain elements. Equivalently, a concave function is any function for which the hypograph is convex. The class of concave functions is in a sense the opposite of the class of convex functions. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap, or upper convex. Definition A real-valued function f on an interval (or, more generally, a convex set in vector space) is said to be ''concave'' if, for any x and y in the interval and for any \alpha \in ,1/math>, :f((1-\alpha )x+\alpha y)\geq (1-\alpha ) f(x)+\alpha f(y) A function is called ''strictly concave'' if :f((1-\alpha )x+\alpha y) > (1-\alpha ) f(x)+\alpha f(y) for any \alpha \in (0,1) and x \neq y. For a function f: \mathbb \to \mathbb, this second definition merely states that for ev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Utility Hypothesis
The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour. The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e., the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities). The summarised formula for expected utility is U(p)=\sum u(x_k)p_k where p_k is the probability that outcome indexed by k with payoff x_k is realized, and function ''u'' expresses the utility of each respective payoff. Graphically the curvature of the u function captures the agent's risk attitude. For example, imagine you’re offered a choice between receiving $50 for sure, or flipping a coin to win $100 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk Aversion
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome. Risk aversion explains the inclination to agree to a situation with a lower average payoff that is more predictable rather than another situation with a less predictable payoff that is higher on average. For example, a risk-averse investor might choose to put their money into a bank account with a low but guaranteed interest rate, rather than into a stock that may have high expected returns, but also involves a chance of losing value. Example A person is given the choice between two scenarios: one with a guaranteed payoff, and one with a risky payoff with same average value. In the former scenario, the person receives $50. In the uncertain scenario, a coin is flipped to decide whether the person receives $100 or nothing. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Economic Theory
The ''Journal of Economic Theory'' is a bimonthly peer-reviewed academic journal covering the field of economic theory. Karl Shell has served as editor-in-chief of the journal since it was established in 1968. Since 2000, he has shared the editorship with Jess Benhabib, Alessandro Lizzeri, Christian Hellwig, and more recently with Alessandro Pavan, Ricardo Lagos (economist), Ricardo Lagos, Marciano Siniscalchi, and Xavier Vives. The journal is published by Elsevier. In 2020, Tilman Börgers was chief editor of the journal. Abstracting and indexing According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 1.458. See also *List of economics journals References External links * Economics journals Elsevier academic journals Academic journals established in 1969 English-language journals Bimonthly journals {{econ-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
