The line of the solution: "In particular, very prudent assumptions would transfer higher amounts to shareholders, to the detriment of policyholders." I understand that the amount paid to SH is driven by the bonuses declared to PH so how can the company potentially abuse this (pointed out in previous paragraph of solution). Aren't they paid amounts relative to each other? (ignoring the timing difference) Also I thought that bonuses were declared on statutory surpluses - wouldn't making the reserves more prudent reduce the level of bonuses that could be declared?
Starting with your second question: I think your statement implicitly assumes that surpluses, once they arise, are declared as bonuses. However though bonuses are declared from surpluses there isn't an exact correlation due to smoothing. Strengthening reserving basis would defer surpluses but bonuses may not necessary be deferred. Going back to the first question: Yes, ShT is expressed relative to policyholder bonuses via the cost of bonus (COB), e.g. 1/9*COB. However, the shareholder's share of this distribution is valued on statutory basis (e.g. using a lower discount rate than an earned rate on backing assets)which places a higher value than their realistic entitlement. So instead of the stated 90:10 say, shareholders may end up getting 12%, implying 88% goes to policyholders. Hope it helps
