Lévy processIn probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random, in which displacements in pairwise disjoint time intervals are independent, and displacements in different time intervals of the same length have identical probability distributions.
Independent incrementsIn probability theory, independent increments are a property of stochastic processes and random measures. Most of the time, a process or random measure has independent increments by definition, which underlines their importance. Some of the stochastic processes that by definition possess independent increments are the Wiener process, all Lévy processes, all additive process and the Poisson point process.
Brownian motionBrownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often itself called "Brownian motion", even in mathematical sources. This motion pattern typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain.
Stochastic processCollection of random variablesA computer-simulated realization of a Wiener or Brownian motion process on the surface of a sphere. The Wiener process is widely considered the most studied and central stochastic process in probability theory.In probability theory and related fields a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time.
CàdlàgIn mathematics, a càdlàg (French: continue à droite, limite à gauche), RCLL ("right continuous with left limits"), or corlol ("continuous on (the) right, limit on (the) left") function is a function defined on the real numbers (or a subset of them) that is everywhere right-continuous and has left limits everywhere.Stationary incrementsIn probability theory, a stochastic process is said to have stationary increments if its change only depends on the time span of observation, but not on the time when the observation was started.
Mathematical financeApplication of mathematical and statistical methods in finance Part of a series onFinance Markets Assets Asset (economics) Bond Asset growth Capital asset Commodity Derivatives Domains Equity Foreign exchange Money Over-the-counter Private equity Real estate Spot Stock Participants Angel investor Bull (stock market speculator) Financial planner Investor institutional Retail Speculator Locations Financial centres Offshore financial centres Conduit and sink OFCs Instruments Bond Cash Collateralized debt obligation Credit default swap Time deposit (certificate of deposit) Credit line Deposit Derivative Futures contract Indemnity Insurance Letter of credit Loan Mortgage Option (callexoticput) Performance bonds Repurchase agreement Stock Security Syndicated loan Synthetic CDO Corporate General Accounting Audit Capital budgeting Capital structure Corporate finance Credit rating agency Enterprise risk management Enterprise value Risk management Financial statements Transactions Leveraged buyout Mergers and acquisitions Structured finance Venture capital Taxation Base erosion and profit shifting (BEPS) Corporate tax haven Tax inversion Tax haven Transfer pricing Personal Credit / Debt Employment contract Financial planning RetirementStudent loan Public Government spending Final consumption expenditure OperationsRedistribution Transfer payment Government revenue TaxationDeficit spending Budget (balance)Debt Non-tax revenue Warrant of payment Banking Central bank Deposit account Fractional-reserve Full-reserve Investment banking Loan Money supply Lists of banks Bank regulation Banking license Basel Committee on Banking Supervision Bank for International Settlements Financial Stability Board Deposit insurance Separation of investment and retail banking Regulation · Financial law International Financial Reporting Standards ISO 31000 Professional certification Fund governance Economic history Private equity and venture capital Recession Stock market bubble Stock market crash Accounting scandals Outline Business and Economics portal Money portalvte Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field.
Norbert WienerNorbert Wiener (November 26, 1894 – March 18, 1964) was an American computer scientist, mathematician, and philosopher. He became a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher in stochastic and mathematical noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.
MathematicsField of knowledgeIlluminated letter P at the beginning of Adelard of Bath's translation of Euclid's Elements, which starts "Punctum est illud cui pars non est" ('A point is that which has no part'). Geometry is shown personified as a woman, following Martianus Capella's De nuptiis Philologiae et Mercurii.Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities.Discrete time and continuous timeIn mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled.
Applied mathematicsApplied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, social science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.
EconomyAn economy is an area of the production, distribution and trade, as well as consumption of goods and services. In general, it is defined as a social domain that emphasize the practices, discourses, and material expressions associated with the production, use, and management of resources.*As an Amazon Associate I earn from qualifying purchases.