Theoretical definitionA theoretical definition defines a term in an academic discipline, functioning as a proposal to see a phenomenon in a certain way. A theoretical definition is a proposed way of thinking about potentially related events. Theoretical definitions contain built-in theories; they cannot be simply reduced to describing a set of observations. The definition may contain implicit inductions and deductive consequences that are part of the theory. A theoretical definition of a term can change, over time, based on the methods in the field that created it.
Fermat's theorem (stationary points)In mathematics, Fermat's theorem (also known as interior extremum theorem) is a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function's derivative is zero at that point). Fermat's theorem is a theorem in real analysis, named after Pierre de Fermat. By using Fermat's theorem, the potential extrema of a function , with derivative , are found by solving an equation in .
Minimum description lengthMinimum Description Length (MDL) is a model selection principle where the shortest description of the data is the best model. MDL methods learn through a data compression perspective and are sometimes described as mathematical applications of Occam's razor. The MDL principle can be extended to other forms of inductive inference and learning, for example to estimation and sequential prediction, without explicitly identifying a single model of the data.
Trading strategyIn finance, a trading strategy is a fixed plan that is designed to achieve a profitable return by going long or short in markets. The main reasons that a properly researched trading strategy helps are its verifiability, quantifiability, consistency, and objectivity. For every trading strategy one needs to define assets to trade, entry/exit points and money management rules. Bad money management can make a potentially profitable strategy unprofitable. Trading strategies are based on fundamental or technical analysis, or both.
Fermat's principleFermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. Fermat's principle states that the path taken by a ray between two given points is the path that can be traveled in the least time. First proposed by the French mathematician Pierre de Fermat in 1662, as a means of explaining the ordinary law of refraction of light (Fig. 1), Fermat's principle was initially controversial because it seemed to ascribe knowledge and intent to nature.
Computational financeComputational finance is a branch of applied computer science that deals with problems of practical interest in finance. Some slightly different definitions are the study of data and algorithms currently used in finance and the mathematics of computer programs that realize financial models or systems. Computational finance emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. It is an interdisciplinary field between mathematical finance and numerical methods.
InfographicInfographics (a clipped compound of "information" and "graphics") are graphic visual representations of information, data, or knowledge intended to present information quickly and clearly. They can improve cognition by utilizing graphics to enhance the human visual system's ability to see patterns and trends. Similar pursuits are information visualization, data visualization, statistical graphics, information design, or information architecture.
Securities fraudSecurities fraud, also known as stock fraud and investment fraud, is a deceptive practice in the stock or commodities markets that induces investors to make purchase or sale decisions on the basis of false information. The setups are generally made to result in monetary gain for the deceivers, and generally result in unfair monetary losses for the investors. They are generally violating securities laws. Securities fraud can also include outright theft from investors (embezzlement by stockbrokers), stock manipulation, misstatements on a public company's financial reports, and lying to corporate auditors.
History of mathematicsThe history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.
Quantitative behavioral financeQuantitative behavioral finance is a new discipline that uses mathematical and statistical methodology to understand behavioral biases in conjunction with valuation. The research can be grouped into the following areas: Empirical studies that demonstrate significant deviations from classical theories. Modeling using the concepts of behavioral effects together with the non-classical assumption of the finiteness of assets. Forecasting based on these methods. Studies of experimental asset markets and use of models to forecast experiments.
