Lecture%204%20Annotated - Life Insurance and Superannuation...

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Unformatted text preview: Life Insurance and Superannuation Models Week 4: Net Premium Reserves March 21, 2011 1 / 24 Week 4: Net Premium Reserves Summary Insurance reserves What are they? How do we calculate them? Why are they important? Net premium reserves Prospective calculation of reserves Retrospective calculation of reserves Equivalence between prospective and retrospective References Chapter 7 (Bowers, et al.), Chapter 6 (Gerber), and CT5 Chapter 5 ACTL3002: Week 4 2 Insurance reserves Money set aside to be able to cover insurers future financial obligations as promised through the insurance contract. Reserves show up as a liability item in the balance sheet; Increases in reserves are an expense item in the income statement. Reserve calculations may vary because of: Purpose of reserve valuation: statutory (solvency), GAAP (realistic, shareholders/investors), mergers/acquisitions Assumptions and basis (mortality, interest) - may be prescribed Actuary is responsible for preparing an Actuarial Opinion and Memorandum: that the companys assets are sufficient to back reserves. Reserves are more often called provisions in Europe. ACTL3002: Week 4 3 Why hold reserves? For several life insurance contracts: The expected cost of paying the benefits generally increases over the contract term; but The periodic premiums used to fund these benefits are level. The portion of the premiums not required to pay expected cost in the early years are therefore set aside (or provisioned) to fund the expected shortfall in the later years of the contract. Reserves also help reduce cost of benefits as they also earn interest while being set aside. Although reserves are usually held on a per contract basis, it is still the overall responsibility of the actuary to ensure that in the aggregate, the companys assets are enough to back these reserves. ACTL3002: Week 4 4 The insurers prospective loss At any future time t, define the insurers prospective loss to be t L = PVFB t- PVFP t . For most types of policies, it is generally true that for t , t L , i.e. PVFB t PVFP t For our purposes, we shall define the expected value of this prospective loss to be the reserves at time t : t V = E ( t L ) = E ( PVFB t )- E ( PVFP t ) , And it is the (smallest) amount for which the insurer is required to hold to be able to cover future obligations. Note that E( t L ) is actually conditional on the survival of the life ( x ) at time t . Because otherwise, there is no need to hold reserves when policy has been paid out. ACTL3002: Week 4 5 Fully discrete reserves - whole life insurance Consider the case of a (discrete) whole life insurance where the premium P x is paid at the beginning of each year and benefit, $1, is paid at the end of the year of death....
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Lecture%204%20Annotated - Life Insurance and Superannuation...

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