没有人研究这方面的吗？

Of course you can use antithetic variables. Why not?

Geometric Asian is usually used as a control variate for arithmetic Asian.

但用对偶变量技术要求payoff是随机抽样样本的单调函数，

但亚式期权好像又是不能满足这个条件

Suppose we want to calculate the expectation of f using Monte Carlo and z is a standard normal variate.

Antithetic variables can reduce variance if Cov[f(z), f(-z)] < 0. This always true if f is monotonic in z. However, f does not have to be monotonic in z to make the covariance negative. For a complicated function like the Asian option payoff, it is diffcult to show the covariance is negative. But it is equally difficult to show it is negative. So why not still using antithetic variables and hopefully the covariance is negative.

The rule of thumb is that, if you are using pseudo-random numbers, and the expection only involves low momemts, then antithetic variables should always be used, because they are so easy to use. In the worst case, your variance is not reduced, but there is no harm using them. However, do not use antithetic variables if you are using quasi-random numbers.