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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hattendorf's theorem ： ウィキペディア英語版 Hattendorf's theorem Hattendorf's Theorem, attributed to K. Hattendorf (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, Hattendorf's theorem demonstrates that the variation in the present value of the loss of an issued insurance policy can be allocated to the future years during which the insured is still alive. This, in turn, facilitates the management of risk prevalent in such insurance contracts over short periods of time. == Hattendorf's Theorem == The main result of the theorem has three equivalent formulations: where: || Actuarial notation for . |- | $\backslash pi\_j$|| The premium received by the insured in year j. |- | $b\_j$|| The benefit paid to the insured in year j. |- | $L\_h$ || The actuarial present value of the total loss over the remaining life of the policy at time h. |- | $C\_h$ || The present value of the net cash loss from the policy in the year (h, h+1). |- | $v$ || The discount factor for one year. |- | $\backslash Lambda\_h$ || The present value of the net cash loss from the policy plus the change in total liabilities in the year (h, h+1). |- | $V\_h$ || The benefit reserve at time h, equal to $\backslash mathbb(|\; K(x)\; \backslash geq\; h)$. |} In its above formulation, and in particular the first result, Hattendorf's theorem states that the variance of $L\_h$, the insurer's total loss over the remaining life of the policy at time h, can be calculated by discounting the variances of the yearly net losses (cash losses plus changes in net liabilities) $\backslash Lambda\_k$ in future years. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hattendorf's theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.