z****i
发帖数: 406 | 1 问问大家的思路吧～
1） - Monte Carlo: integrate f(x) over [a,b] numerically given a random
number generator.
是说在[a,b]上取n个点，均匀分布的，然后把f在这些点的值加起来，除以n，乘以(b-a
)？
一维情况下，这么做跟用Riemann Sum比有什么优势么？
2） - Monte Carlo: derive the standard error of different variance reduction
techniques(antithetic variables, control variables, etc).
不知道怎么做，某个牛人给点hint吧？
3）- Minimize f(x) = |x-a| + |x-b| + |x-c| + |x-d|
假设a
4）- Numerical analysis: condition of a problem, ill posed problems, error
anal | S*******r
发帖数: 11017 | 2 我的功力不足子弹牙十分之一，所以力所能及地解答一下。
有关第2）题
For antithetic variables, we pick 2 different but correlated sequences of iid N(0,1) or U[0,1] to run the MC simulation--let's say U and U' where U + U'= 1 so rho(U,U')=-1. The estimated price is C1,C2,..., Cn so without variance reduction, its std err is var(C)/n; now we use U to estimate C, and use U' to estimate C', and we take the average (C+C')/2 as the final estimate. Here the new std err is Var[(C+C')/2]=.25*Var(C+C')=.5*Var(C)[1+rho(C,C')] which is small | z****i
发帖数: 406 | 3 多谢大牛，看懂了。
你们真牛，唉。。。 要补的东西真多。
Thank you so much!!!
iid N(0,1) or U[0,1] to run the MC simulation--let's say U and U' where U +
U'= 1 so rho(U,U')=-1. The estimated price is C1,C2,..., Cn so without
variance reduction, its std err is var(C)/n; now we use U to estimate C, and
use U' to estimate C', and we take the average (C+C')/2 as the final
estimate. Here the new std err is Var[(C+C')/2]=.25*Var(C+C')=.5*Var(C)[1+
rho(C,C')] which is smaller than Var(C).
/n; Now let's plug in one more sequence
【在 S*******r 的大作中提到】
: 我的功力不足子弹牙十分之一，所以力所能及地解答一下。
: 有关第2）题
: For antithetic variables, we pick 2 different but correlated sequences of iid N(0,1) or U[0,1] to run the MC simulation--let's say U and U' where U + U'= 1 so rho(U,U')=-1. The estimated price is C1,C2,..., Cn so without variance reduction, its std err is var(C)/n; now we use U to estimate C, and use U' to estimate C', and we take the average (C+C')/2 as the final estimate. Here the new std err is Var[(C+C')/2]=.25*Var(C+C')=.5*Var(C)[1+rho(C,C')] which is small
| o******e
发帖数: 74 | 4 第一题难道是MC方便给出std. err?
第三题我做的是d+c-b-a @ 区间[b,c]，不一定对，呵呵。
-a
reduction
【在 z****i 的大作中提到】
: 问问大家的思路吧～
: 1） - Monte Carlo: integrate f(x) over [a,b] numerically given a random
: number generator.
: 是说在[a,b]上取n个点，均匀分布的，然后把f在这些点的值加起来，除以n，乘以(b-a
: )？
: 一维情况下，这么做跟用Riemann Sum比有什么优势么？
: 2） - Monte Carlo: derive the standard error of different variance reduction
: techniques(antithetic variables, control variables, etc).
: 不知道怎么做，某个牛人给点hint吧？
: 3）- Minimize f(x) = |x-a| + |x-b| + |x-c| + |x-d|
|
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