x******a
发帖数: 6336 | 1 7匹马比赛，1元赌注，如果赌第1匹赢了给你3元，如果赌第2匹赢了给你4元，。。。如
果赌第7匹马赢了给你9元， 你有200元，该怎么下注？ | D*****a
发帖数: 2847 | 2 有arbitrage
可以short吗？
【在 x******a 的大作中提到】
: 7匹马比赛，1元赌注，如果赌第1匹赢了给你3元，如果赌第2匹赢了给你4元，。。。如
: 果赌第7匹马赢了给你9元， 你有200元，该怎么下注？
| x********9
发帖数: 31 | 3 It depends on your risk preference. I did not quite get what you mean...You
get four if you get both the first one and the second one right or just the
second one right?
If you are risk-neutral, and you get 4 when you get the second right, etc...
Then you should use backward induction.
Assume your value function to be V_i(W) at the ith round before choosing how
much to bet for the i+1 th round.
V_7(W) = W
V_6(W)= 4 W
V_5(W) = max_{w} 0.5*V_6(W + 8w ) + 0.5*V_6(W-w) =
You should obtain you will always bet everything you have.
But if you are risk averse, solution will be very different. |
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