Iām not sure if this would just create other technical problems I havenāt thought of, but one solution could just be to replace ābest possibleā with, e.g., āex ante 99.9th percentileā. Then you wouldnāt have this discontinuity from changing the max, but it captures basically the same intuition?
(One problem is that itās not obvious what the threshold should be. But my guess is that when people are trying to figure out the relevant denominator for PVBPF theyāre usually implicitly truncating the probability distribution over outcomes somewhere anyway, since it seems very hard to reason about the absolute maximum.)
Claude also suggested something like a conditional expectation of the upper tail, e.g. E[V|Vā„q0.999], which seems interesting but Iāve not thought carefully about.
Iām not sure if this would just create other technical problems I havenāt thought of, but one solution could just be to replace ābest possibleā with, e.g., āex ante 99.9th percentileā. Then you wouldnāt have this discontinuity from changing the max, but it captures basically the same intuition?
(One problem is that itās not obvious what the threshold should be. But my guess is that when people are trying to figure out the relevant denominator for PVBPF theyāre usually implicitly truncating the probability distribution over outcomes somewhere anyway, since it seems very hard to reason about the absolute maximum.)
Claude also suggested something like a conditional expectation of the upper tail, e.g. E[V|Vā„q0.999], which seems interesting but Iāve not thought carefully about.