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In full generality, the accelerated failure time model can be specified as [2] (|) = ()where denotes the joint effect of covariates, typically = ([+ +]). (Specifying the regression coefficients with a negative sign implies that high values of the covariates increase the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)
Dynamic financial analysis (DFA) is method for assessing the risks of an insurance company using a holistic model as opposed to traditional actuarial analysis, which analyzes risks individually. Specifically, DFA reveals the dependencies of hazards and their impacts on the insurance company's financial well being as a whole such as business mix ...
Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory , reliability analysis or reliability engineering in engineering , duration analysis or duration modelling in economics ...
This is the survival function for Weibull distribution. For α = 1, it is same as the exponential distribution. Another famous example is when the survival model follows Gompertz–Makeham law of mortality. [2] In this case, the force of mortality is = +
This is particularly the case in non-life insurance (e.g. the pricing of motor insurance can allow for a large number of risk factors, which requires a correspondingly complex table of expected claim rates). However the expression "life table" normally refers to human survival rates and is not relevant to non-life insurance.
The computations of life insurance premiums and reserving requirements are rather complex, and actuaries developed techniques to make the calculations as easy as possible, for example "commutation functions" (essentially precalculated columns of summations over time of discounted values of survival and death probabilities). [24]
"Operational Continuity and Additivity of Operational Risk" (PDF). Archived from the original (PDF) on 2013-06-17. Tyson Macaulay (2008). "Metrics and Operational Continuity" (PDF). Archived from the original (PDF) on 2013-06-17. Operational Risk Consortium is a consortium that collects and analyzes operational risk loss data for the insurance ...
As a practical matter, indices or spot or futures market prices may be used in place of macro-economic factors, which are reported at low frequency (e.g. monthly) and often with significant estimation errors. Market indices are sometimes derived by means of factor analysis. More direct "indices" that might be used are: short-term interest rates;