InsuranceInsurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge against the risk of a contingent or uncertain loss. An entity which provides insurance is known as an insurer, insurance company, insurance carrier, or underwriter. A person or entity who buys insurance is known as a policyholder, while a person or entity covered under the policy is called an insured.
Risk aversionIn economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome. Risk aversion explains the inclination to agree to a situation with a more predictable, but possibly lower payoff, rather than another situation with a highly unpredictable, but possibly higher payoff.
Risk assessmentRisk assessment determines possible mishaps, their likelihood and consequences, and the tolerances for such events. The results of this process may be expressed in a quantitative or qualitative fashion. Risk assessment is an inherent part of a broader risk management strategy to help reduce any potential risk-related consequences. More precisely, risk assessment identifies and analyses potential (future) events that may negatively impact individuals, assets, and/or the environment (i.e. hazard analysis).
ReinsuranceReinsurance is insurance that an insurance company purchases from another insurance company to insulate itself (at least in part) from the risk of a major claims event. With reinsurance, the company passes on ("cedes") some part of its own insurance liabilities to the other insurance company. The company that purchases the reinsurance policy is referred to as the "ceding company" or "cedant". The company issuing the reinsurance policy is referred to as the "reinsurer".
Risk managementRisk management is the identification, evaluation, and prioritization of risks (defined in ISO 31000 as the effect of uncertainty on objectives) followed by coordinated and economical application of resources to minimize, monitor, and control the probability or impact of unfortunate events or to maximize the realization of opportunities.
Fixed-point theoremIn mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. The Banach fixed-point theorem (1922) gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point.
RiskIn simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environment), often focusing on negative, undesirable consequences. Many different definitions have been proposed. The international standard definition of risk for common understanding in different applications is "effect of uncertainty on objectives".
Fixed-point iterationIn numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.
Kakutani fixed-point theoremIn mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for a set-valued function defined on a convex, compact subset of a Euclidean space to have a fixed point, i.e. a point which is mapped to a set containing it. The Kakutani fixed point theorem is a generalization of the Brouwer fixed point theorem. The Brouwer fixed point theorem is a fundamental result in topology which proves the existence of fixed points for continuous functions defined on compact, convex subsets of Euclidean spaces.
Risk premiumA risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky return less the risk-free return, as demonstrated by the formula below. Where is the risky expected rate of return and is the risk-free return. The inputs for each of these variables and the ultimate interpretation of the risk premium value differs depending on the application as explained in the following sections.
