Terence Tao on Nostr: Anyway, if we assume that the external −5±10 shock is uncorrelated with one's ...
Anyway, if we assume that the external −5±10 shock is uncorrelated with one's previous risks (which, by the way, is a non-trivial assumption, and worth further inspection if one wants to make the model more complex and realistic), then the risk-reward calculus of the safe option moves from 5±3 to 0±√(10²+3²)=0±10.44, while the bold option moves from 9±10 to 4±√(10²+10²)=4±14.14. The value at risk for the safe option is -10.44, while the bold option is now -10.14. While neither option is particularly appetizing, the bold option is now marginally better.
Of course, these were artificial numbers plugged into an overly simple model, but what is important is not the specific numbers, but the broader point, which is this: in times of great uncertainty, the relative value of "playing it safe" is reduced, since - for better or for worse - no option can now reduce risk to truly safe levels. And so, it can become more rational to think and act more boldly.
(4/4)
Of course, these were artificial numbers plugged into an overly simple model, but what is important is not the specific numbers, but the broader point, which is this: in times of great uncertainty, the relative value of "playing it safe" is reduced, since - for better or for worse - no option can now reduce risk to truly safe levels. And so, it can become more rational to think and act more boldly.
(4/4)