QuantileIn statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities or dividing the observations in a sample in the same way. Common quantiles have special names, such as quartiles (four groups), deciles (ten groups), and percentiles (100 groups).
Value at riskValue at risk (VaR) is a measure of the risk of loss of investment/capital. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses.
Absolute valueIn mathematics, the absolute value or modulus of a real numberx{\displaystyle x}, denoted |x|{\displaystyle |x|}, is the (non-negative) magnitudeof x{\displaystyle x}measured without regard to its sign. Namely, |x|=x{\displaystyle |x|=x} if x{\displaystyle x} is a positive number, and |x|=−x{\displaystyle |x|=-x} if x{\displaystyle x} is negative (in which case −x{\displaystyle -x} is positive), and |0|=0{\displaystyle |0|=0}.Coherent risk measureIn the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have. A coherent risk measure is a function that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance.Risk measureIn financial mathematics, a risk measure assigns a numerical value to the risk associated with a financial position or portfolio. In financial management and insurance, risk measures are often used to determine capital reserve requirements to mitigate downside risk to make it acceptable to regulators. In recent years attention has turned to convex and coherent risk measurement.
Actuarial scienceActuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, pension, finance, investment, psychology, medicine, and other industries and professions. Actuaries are professionals trained in this discipline. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations focused in fields such as probability and predictive analysis.Lp spaceIn mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910). Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces.
Downside riskDownside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk can be measured either with downside beta or by measuring lower semi-deviation.Mathematical financeMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
Financial riskAny of various types of risk associated with financing Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financial loss and uncertainty about its extent.Credit riskCredit risk is the chance that a borrower does not repay a loan or fulfill a loan obligation. For lenders the risk includes late or lost interest and principal payment, leading to disrupted cash flows and increased collection costs. The loss may be complete or partial. In an efficient market, higher levels of credit risk will be associated with higher borrowing costs.Market riskMarket risk is the risk of losses in positions arising from movements in market variables like prices and volatility. There is no unique classification as each classification may refer to different aspects of market risk.*As an Amazon Associate I earn from qualifying purchases.