Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
Market (economics)In economics, a market is a composition of systems, institutions, procedures, social relations or infrastructures whereby parties engage in exchange. While parties may exchange goods and services by barter, most markets rely on sellers offering their goods or services (including labour power) to buyers in exchange for money. It can be said that a market is the process by which the prices of goods and services are established. Markets facilitate trade and enable the distribution and allocation of resources in a society.
Dominance (economics)Market dominance is the control of a economic market by a firm. A dominant firm possesses the power to affect competition and influence market price. A firms' dominance is a measure of the power of a brand, product, service, or firm, relative to competitive offerings, whereby a dominant firm can behave independent of their competitors or consumers, and without concern for resource allocation. Dominant positioning is both a legal concept and an economic concept and the distinction between the two is important when determining whether a firm's market position is dominant.
Generalized polygonIn mathematics, a generalized polygon is an incidence structure introduced by Jacques Tits in 1959. Generalized n-gons encompass as special cases projective planes (generalized triangles, n = 3) and generalized quadrangles (n = 4). Many generalized polygons arise from groups of Lie type, but there are also exotic ones that cannot be obtained in this way. Generalized polygons satisfying a technical condition known as the Moufang property have been completely classified by Tits and Weiss.
Market economyA market economy is an economic system in which the decisions regarding investment, production and distribution to the consumers are guided by the price signals created by the forces of supply and demand. The major characteristic of a market economy is the existence of factor markets that play a dominant role in the allocation of capital and the factors of production.
Market structureMarket structure, in economics, depicts how firms are differentiated and categorised based on the types of goods they sell (homogeneous/heterogeneous) and how their operations are affected by external factors and elements. Market structure makes it easier to understand the characteristics of diverse markets. The main body of the market is composed of suppliers and demanders. Both parties are equal and indispensable. The market structure determines the price formation method of the market.
Numerical cognitionNumerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. As with many cognitive science endeavors, this is a highly interdisciplinary topic, and includes researchers in cognitive psychology, developmental psychology, neuroscience and cognitive linguistics. This discipline, although it may interact with questions in the philosophy of mathematics, is primarily concerned with empirical questions.
Geometric Brownian motionA geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the Black–Scholes model.
Free marketIn economics, a free market is an economic system in which the prices of goods and services are determined by supply and demand expressed by sellers and buyers. Such markets, as modeled, operate without the intervention of government or any other external authority. Proponents of the free market as a normative ideal contrast it with a regulated market, in which a government intervenes in supply and demand by means of various methods such as taxes or regulations.
Local volatilityA local volatility model, in mathematical finance and financial engineering, is an option pricing model that treats volatility as a function of both the current asset level and of time . As such, it is a generalisation of the Black–Scholes model, where the volatility is a constant (i.e. a trivial function of and ). Local volatility models are often compared with stochastic volatility models, where the instantaneous volatility is not just a function of the asset level but depends also on a new "global" randomness coming from an additional random component.
