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MTHEL 131 (32)

MTHEL131 textbook notes (29)

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Mathematics Electives
David Kohler

MTHEL131 Textbook notes – Life and Health Insurance 13e (Black and Skipper) Chapter 29 Erin Edward Life Insurance Reserves and cash values Reserves  Most reserves reflect an insurer’s obligation to its customers, but some relate to investments  Policy reserves are liabilities that represent the amount that will be needed to pay future policy benefits  Cash surrender values are related to policy reserves (represent policy owners’ demand claims against the insurer’s assets Origin and Definition of the Policy Reserve  Excess funds not used immediately to pay policy claims must be recognized by the insurer, and preserved for the benefit of all the policy owners until needed at some future date.  Formula statutory policy reserve: amount (with future net premiums and interest) sufficient to pay future claims o Ignore insurer expenses and lapse rates o Based solely on state-sanctioned mortality and interest assumptions  Reserve calculations (valuations): o Use mortality table and interest rate, calculate net premium o Selection of policy duration for which the reserve is needed o Prospective or retrospective method  No relationship with insurer’s past experience  Minimum reserve standards establish definite methods of valuing policy liabilities.  Policy reserve is a liability to the insurance company Methods of calculation: 1. Retrospective method  Looks at policy’s past premiums and benefits to determine policy reserves.  policy reserve = accumulated value of net premiums - accumulated cost of insurance 2. group approach:  reserve arises from the payment of level net premium in excess of that needed to meet current mortality costs.  Premiums in the early policy years are more than needed to pay death claims that are assumed. Create a fund for years later where death claims rise sharply and premiums are insufficient. 3. Individual approach:  Retrospective terminal reserve= (net premium of year in question + terminal reserve of previous year) x interest rate – cost of insurance for net amount at risk  Net amount at risk= death benefit – terminal reserve at end of policy year  Cost of insurance (contribution from each insured in a year)= net amount at risk x tabular probability of death for the year MTHEL131 Textbook notes – Life and Health Insurance 13e (Black and Skipper) Chapter 29 Erin Edward 4. Prospective reserve:  more common  reserve is the balancing factor in the basic insurance equation (difference between present value of expected future benefits and the present value of expected future net premiums)  present value of future benefits = present value of future net premiums  as soon as contract goes in force, first premium is paid, present value of future net premiums goes down  the difference of these two quantities is a measure of the obligation (reserve) of the insurer  (See formulas on pg. 741)  Present value of future net premiums involves the determination of the original net level annual premium applicable to the contract, multiplied by the present value of a temporary life annuity due of 1 for the remaining premium-paying period. Terminal, initial and mean reserves  The previous calculations represent the terminal reserves o Used for determining dividends under participating policies o Determine non-forfeiture values o Form of reinsurance based on yearly renewable term insurance of net amount at risk  initial reserve: reserve at the beginning of the policy year o Terminal reserve for the preceding year, increased by the net level annual premium for current year o Used for determining dividends under participating policies  Mean reserve: average of the terminal reserve and the initial reserve for any year of valuation o Used for annual statements of life insurance Significance of Actuarial Assumptions  Assumptions are reflected in the mortality table  Other assumptions are made in reserve valuations 1. Mortality: o Change in mortality affects number of deaths at a given age, as well as number of surviving at subsequent ages o Net level premium: spread over premium-paying period o Not uniform from age to age, and duration to duration, results in either increase or decrease in reserve 2. Interest: o Rate of interest assumed is decreased, increase in reserves
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