OEP Example
The example at the end of the article suggests we can estimate the OEP of 10m to be less than 1% by linear approximation. But p3 is greater than 1%, so we can deduce OEP(10,999,999) is over 1% too, right?
The example at the end of the article suggests we can estimate the OEP of 10m to be less than 1% by linear approximation. But p3 is greater than 1%, so we can deduce OEP(10,999,999) is over 1% too, right?
Comments
I guess my question is whether linear interpolation is appropriate in these discrete scenarios. If we do use it, maybe the interpolation should be between the higher percentages rather than the lower ones, e.g. between OEP(10.9M) and OEP(8.9M) rather than 11 and 9.
Following a strict mathematical interpretation of the OEP(L_i) formula we have OEP(9m) = OEP(9,000,001) = ... = OEP(10,999,999) = 1.4% because the distribution is discrete. Ideally, we would simulate more events using say different storm characteristics such as intensity, maximum wind speed etc, which would generate losses within the range 9m to 11m. Having more data would give a better understanding of the curve the interpolation. But that's not very practical or kind for on an exam...
Linear interpolation is probably the most defensible way of interpolating to allow us to recognize the greater the loss threshold the lower the probability of us having a loss exceeding it. Other forms of interpolation could be used to give a more conservative estimate/margin for error.