Likelihood-ratio testIn statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models, specifically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods. If the constraint (i.e., the null hypothesis) is supported by the observed data, the two likelihoods should not differ by more than sampling error. Thus the likelihood-ratio test tests whether this ratio is significantly different from one, or equivalently whether its natural logarithm is significantly different from zero.
Investment fundAn investment fund is a way of investing money alongside other investors in order to benefit from the inherent advantages of working as part of a group such as reducing the risks of the investment by a significant percentage. These advantages include an ability to: hire professional investment managers, who may offer better returns and more adequate risk management; benefit from economies of scale, i.e., lower transaction costs; increase the asset diversification to reduce some unsystematic risk.
Ratio testIn mathematics, the ratio test is a test (or "criterion") for the convergence of a series where each term is a real or complex number and an is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test. The usual form of the test makes use of the limit The ratio test states that: if L < 1 then the series converges absolutely; if L > 1 then the series diverges; if L = 1 or the limit fails to exist, then the test is inconclusive, because there exist both convergent and divergent series that satisfy this case.
Complexity classIn computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements.
Pension fundA pension fund, also known as a superannuation fund in some countries, is any program, fund, or scheme which provides retirement income. Pension funds typically have large amounts of money to invest and are the major investors in listed and private companies. They are especially important to the stock market where large institutional investors dominate. The largest 300 pension funds collectively hold about USD6trillioninassets.In2012,PricewaterhouseCoopersestimatedthatpensionfundsworldwideholdover33. Fund administrationFund administration is the name given to the execution of back-office activities including fund accounting, financial reporting, net asset value calculation, capital calls, distributions, investor communications and other functions carried out in support of an investment fund, which may take the form of a traditional mutual fund, a hedge fund, a private equity fund, a venture capital fund, a pension fund, a unit trust, or other pooled investment vehicle.
Fund of fundsA "fund of funds" (FOF) is an investment strategy of holding a portfolio of other investment funds rather than investing directly in stocks, bonds or other securities. This type of investing is often referred to as multi-manager investment. A fund of funds may be "fettered", meaning that it invests only in funds managed by the same investment company, or "unfettered", meaning that it can invest in external funds run by other managers.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Quantum complexity theoryQuantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics. It studies the hardness of computational problems in relation to these complexity classes, as well as the relationship between quantum complexity classes and classical (i.e., non-quantum) complexity classes. Two important quantum complexity classes are BQP and QMA.
Uniform convergenceIn the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions converges uniformly to a limiting function on a set as the function domain if, given any arbitrarily small positive number , a number can be found such that each of the functions differs from by no more than at every point in .
Index fundAn index fund (also index tracker) is a mutual fund or exchange-traded fund (ETF) designed to follow certain preset rules so that the fund can replicate the performance ("track") of a specified basket of underlying investments. While index providers often emphasize that they are for-profit organizations, index providers have the ability to act as "reluctant regulators" when determining which companies are suitable for an index.
Σ-algebraIn mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair is called a measurable space. The σ-algebras are a subset of the set algebras; elements of the latter only need to be closed under the union or intersection of finitely many subsets, which is a weaker condition.
