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最近在看卡尼曼的PROSPECT THEORY 1979（263~292）
有个不明白的地方，还请大家指教：
关于PROBABILISTIC INSURANCE（这个……怎么翻译比较好？）的270页
In contrast to these data, expected utility theory (with a concave u) implies that probabilistic insurance is superior to regular insurance. That is, if at asset position w one is just willing to pay a premium y to insure against a probability p of losing x, then one should definitely be willing to pay a smaller premium ry to reduce the probability of losing x from p to (1 - r)p, 0 < r < 1. Formally, if one is indifferent between (w -x, p; w, 1 -p) and (w - y), then one should prefer probabilistic insurance (w -x, (1 - r)p; w - y, rp; w - ry, 1 -p) over regular insurance (w - y).

To prove this proposition, we show that

pu ( w - x ) + ( l - p ) u ( w ) = u ( w -y ) （1）

implies

(1-r)pu(w -x)+rpu(w -y)+(l-p)u(w-ry)>u(w -y). ???由（1）可以得到这个么？这个不是要证明的结论么？

Without loss of generality, we can set u(w -x) = 0 and u(w) = 1. Hence, u(w - y) = 1 -p, and we wish to show that

rp(1-p)+(1-p)u(w-ry)>1-p or u(w-ry)>1-rp 结论证明什么了？没看明白。

which holds if and only if u is concave.

这段证明不是很明白，请解释一下。还有为什么根据预期效用理论PROBABILISTIC INSURANCE比常规保险更好，因为人们风险回避？
本人对行为金融学很感兴趣，但是苦于自身所学粗浅，才刚刚入门，所以问题难免幼稚，希望各位大大能耐心讲解，谢谢~

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关键词：Probability proposition Insurance Different bability 请教