个人浅见，请轻拍。实分析有用，因为是现代概率论的基础，涉及到风险度量方面，从而和各种资产定价有关系。复变貌似没有，好像复变的研究好久没啥进展了，因为大家发现实分析能扯上金融从而能搞到钱，所以大家都去做实分析了，空间群什么的不懂。金融的话除了实分析再就是偏微分方程，随机微分，蒙特卡洛啥的，泛函最好也了解下。

   首先谢谢你的回复。
  你指的偏微分方程是Partial differential equation吧 那个着实很复杂研究wave的，但是real analysis大部分我接触到的基本是研究极限的证明等等 没有感觉到跟风险度量有什么关系，是不是我学的太肤浅了？ 还有你指的资产定价是 portfolio theory 和 pricing model吗 如果是的话 跟实分析有什么联系呢？

我这主要也是道听途说为主哈。实变的话连着测度论，测度论连着概率论，然后就是研究如何测定风险，在之后就是衍生品定价，具体定价涉及到pde、sde，bsde啥的。听过一个大神老师说，不学实变，不学随机，不学微分方程，学的哪门子金融。。。那老师搞风险的，开的课都和蒙特卡洛有关。。。
在下才疏学浅，仅为抛砖引玉。

谢谢哈

No direct relationship and application, but may help you to have a deeper understanding of probability theory.
They may have some use in stochastic calculus such as the sigma field in conditional expectation or defining an integral on a measure. And also very helpful in change of measure theory. So I also recommend measure theory.

Anyway, one can study finance without these knowledges, but if you have, it is better. Perhaps you spend a lot of time study all of these ( real analysis, complex analysis),and you may find that only a few part is useful in finance. So this depends on your interest.

Instead, some skills in physics is much more useful, since they are more practical. Such as Fourier transform or solving pde in practice while mathematics mostly only discuss the existence and uniqueness of the pde's solution.
best,