最近看一篇Daniel 伯努利在十八世紀用拉丁文寫的一篇文章，在1954年翻成英文，題目是:
Exposition of a New Theory on the management of risk
伯努利是很有名的學術家族，父子堂兄弟等人，在數學，醫學，數學，統計，物理都有新發現。
Daniel伯努利這篇文章批評了傳統以算數期望值來評定價值的觀念，主張應該要對風險加以調整，尤其要考慮"累積"的觀念，基本上就是算出幾何平均數，和期初財富的差異部分就是風險所在。
原文英文翻譯是(我不懂拉丁文)：
Any gain must be added to the fortunepreviously possessed, then this sum must be raised to the power given by the number of possible ways in which the gain may be obtained; these terms should then be multiplied together. Then of this product a root must be extracted the degree of which is given by the number of all possible cases, and finally the value of the initial possessions must be subtracted therefrom; what then remains indicates the value of the risky proposition in question.
這個觀念其實提供給未來公允價值或評價公報中提到Certainty equivalent(確定當量)很重要的理論與實務應用計算基礎。
這理論Daniel伯努利在兩百多年前已提出，但實務上最近才逐漸落實，社會科學的發展與演進，真是漫長啊!
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