Blog post: https://daze68.blogspot.com/2021/03/3-utility-function-3-insurance-and.html ====== 相对风险趋避系数η在资产配置的应用 数学上相对比较复杂 也许不是每位朋友都会认同 让我们尝试一些比较直观的应用 比如说，保险: 假设总资产1000万，其中汽车价值100万 预期一年内平安无事机率99%，发生车祸完全撞毁机率1% 是否该买要价x万元的车体险? If η=1，u(c)=ln(c) 不购买车体险 utility = ln(1000/1000)*0.99 + ln( (1000-100)/1000)*0.01 购买车体险 utility = ln((1000-x)/1000)*0.99 + ln((1000-x)/1000)*0.01 车体险要价小於1.05万元时，购买车体险的utility就会大於不购买 If η=3，u(c)=(c^(1-3)-1)/(1-3) 不购买车体险 utility = ((1000/1000)^(-2)-1)/(-2)*0.99 + (((1000-100)/1000)^(-2)-1)/(-2)*0.01 购买车体险 utility = (((1000-x)/1000)^(-2)-1)/(-2)*0.99 + (((1000-x)/1000)^(-2)-1)/(-2)*0.01 车体险要价小於1.17万元时，购买车体险的utility就会大於不购买 ====== utility function也不只能用在财务规划 举例来说 假设核四发生核灾机率为x 核四商转不发生核灾可让资产增加1% 发生核灾会让资产减少90% 是否该支持核四商转? If η=1，u(c)=ln(c) (1-x)ln(1.01)+x*ln(0.1)==0, solve x => x=0.0043 如果核灾机率大於0.43%，utility就变负 If η=3，u(c)=(c^(1-3)-1)/(1-3) (1-x)*(1.01^(-2)-1)/(-2)+x*(0.1^(-2)-1)/(-2)==0, solve x => x=0.00020 如果核灾机率大於0.02%，utility就变负 即使大家对於财产收益与损失的预期及核灾的发生率相同 在不同的η之下 决定也可能是不同的 -- You got to know when to hold 'em, know when to fold 'em, Know when to walk away and know when to run. You never count your money when you're sittin' at the table. There'll be time enough for countin' when the dealin's done. 'Cause ev'ry hand's a winner and ev'ry hand's a loser, And the best that you can hope for is to die in your sleep." now Ev'ry gambler knows that the secret to survivin' Is knowin' what to throw away and knowing what to keep. --

※ 发信站: 批踢踢实业坊(ptt.cc), 来自: 36.237.73.127 (台湾) ※ 文章网址: https://webptt.com/cn.aspx?n=bbs/CFP/M.1614609645.A.FA8.html ※ 编辑: daze (36.237.73.127 台湾), 03/01/2021 22:54:44