Being a verbose person, I won't tick the boxes above but talk about the options:
Respond publicly and quickly to clarify/explain/refute all points in this allegation.
I have met the person who would do that, but would be shocked if they did. I don;t believe UCB has people who can engage in the nose to nose arguments this would require. They'd turn a small fight into a big lost battle, and they are too smart to do that. My conclusion is independent of whether the allegations are true.
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Ignore. Who gives a damn about some unhappy students.
Colleges are collegiate, some of the staff will be saying that, and to be fair, you can't please every single person you teach. My oldest enemy is a guy I tried to help understand something in 1983, he came to believe that I had him removed from the course, when in fact I was apparently his last shot at staying on it. He still goes into one, if my name comes up.
Ask Fordham MSQF what they did to make "it" go away
Yes, that affair didn't help them at all. I have no clear picture of the damage they did to themselves in this. I suspect I made it worse, I hope so.
Prohibit their students from any forum posting in the future. Put it in the contract.
Some universities do have such things in their statutes, though phrased in language that pre-dates the Internet. Although I'm the oldest person on this site and probably older than a course director who might do it, I keep thinking of such people as dinosaurs when they try this.
That's not an just Internet thing, but started with the invention of the printing press, google on McLibel for what happens when evangelical management unleash lawyers to defend their image.
Quantnet doesn't display names, nor does Wilmott.com, and many other sites. So enforcement is really tough. They might try snooping on your web traffic, or using legal crowbars to force a site to release your name. This would be a mistake. People like me would ensure that a small spat became a major headache, The technology web sites love stories like this, and I'd do what I could to spread the big ugly story of academic bullying. Bankers, and by extension those who train them are not popular.
If you are at a school thinking of doing this, please treat that as a threat.
We eat our own dog food on this...
Paul owns Wilmott.com, by far the largest web site for quants, and you will find criticism not only of his CQF, but his books, his views on finance, and his personal attributes as well as P&D. I have the largest social network of quants through my LinkedIn.com group and the same discipline is followed. We don't delete criticism, partly because of free speech, but also because it only makes things worse.
Economists use the term "reputational capital", in the context of the audit process.
A third party looks at the data, performs checks, and applies publicly disclosed rules to produce a result that can be trusted. The idea is that the third party values their reputation more than the audited organisation can outbid.
That doesn't always work of course, but is usually does, and no one has a better mechanism.
So the way forward is to find a firm or person who enjoys great public trust, understands the system, and whose reputation for integrity has real value for them.
...that's not me.
You may or my not trust me, but anyway I'm an interested party, I teach on the CQF.