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Credibility theory is a branch of actuarial mathematics concerned with determining risk premiums. [1] To achieve this, it uses mathematical models in an effort to forecast the ( expected ) number of insurance claims based on past observations.
Hattendorff's Theorem, attributed to K. Hattendorff (1868), is a theorem in actuarial science that describes the allocation of the variance or risk of the loss random variable over the lifetime of an actuarial reserve. In other words, Hattendorff's theorem demonstrates that the variation in the present value of the loss of an issued insurance ...
The actuarial present value (APV) is the expected value of the present value of a contingent cash flow stream (i.e. a series of payments which may or may not be made). Actuarial present values are typically calculated for the benefit-payment or series of payments associated with life insurance and life annuities. The probability of a future ...
A middle ground of sorts was taken by C. W. Jordan in his Life Contingencies, where he included de Moivre in his section on "Some famous laws of mortality", but added that "de Moivre recognized that this was a very rough approximation [whose objective was] the practical one of simplifying the calculation of life annuity values, which in those ...
The European embedded value (EEV) is an effort by the CFO Forum to standardize the calculation of the embedded value. For this purpose the CFO Forum has released guidelines how embedded value should be calculated. There is a lot of subjectivity involved in calculating the value of a life insurer. Insurance contracts are long-term contracts, so ...
It is generally equal to the actuarial present value of the future cash flows of a contingent event. In the insurance context an actuarial reserve is the present value of the future cash flows of an insurance policy and the total liability of the insurer is the sum of the actuarial reserves for every individual policy.
A common case in literature is to define TVaR and average value at risk as the same measure. [1] Under some formulations, it is only equivalent to expected shortfall when the underlying distribution function is continuous at VaR α ( X ) {\displaystyle \operatorname {VaR} _{\alpha }(X)} , the value at risk of level α {\displaystyle \alpha ...
An immediate consequence is that value at risk might discourage diversification. [1] Value at risk is, however, coherent, under the assumption of elliptically distributed losses (e.g. normally distributed) when the portfolio value is a linear function of the asset prices. However, in this case the value at risk becomes equivalent to a mean ...