Premium calculation for Robbin Present Value Offset method

There is a premium formula for the Robbin Present Value Offset Method that results in a different premium than if you were to calculate it based on the traditional premium formula:
P = (L*(1 + ULAE) + FE)/(1 - VE - profit) where the profit is the load calculated directly from this method.

Does anyone know why you get a different answer from these two formulas or what the logic is here?

The formula you’ve typed out there doesn’t take into account the discounting of losses at all. The point of the present value offset method is to adjust the profit provision from that of a reference line based on the loss payout pattern.

doesn’t account for discounting at all for losses or expenses or premium received patterns or interest earned on reserves and capital (okay I don’t actually remember what Robin’s method is), but this can get as sophisticated as you want if you want to create a generic formula that applies to any insurance products of any duration, not just P&C

Thanks. I will assume that the two formulas are not meant to tie together in any direct way. Good to know there isn’t some derivation of the more complicated premium formula that I was missing.

I use this formula: P = (L+ LAE - Loss*(PVLOBdiscount - PVRefdiscount)) / (1 - VE - U0)
where u0 is the initial starting underwriting profit.

So here you are essentially subtracting out the additional investment income/losses from the losses.

So the two do work together.

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I was surprised when I saw this question. Because I am like I specifically use that formula since you don’t need to remember anything. This is one of the tricks I discussed last year in outpost…

The formula you wrote out is a lot more intuitive than the formula for premium in the Robbin text for this method. Definitely helpful - thanks!