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MTHEL 131 (32)
Chapter 29

Chapter 29 Reading Notes

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Department
Mathematics Electives
Course
MTHEL 131
Professor
David Kohler
Semester
Fall

Description
Chapter 29: Reserves and cash values Reserves Policy Reserves - liabilities that represent the amount expected to be needed to pay future benefits. - Measure of the value of obligations to policy owners (regulated by state) Formula statutory policy reserve - amount that (together with future net premiums and interest) will be sufficient to pay future claims - Ignores expenses and lapse rates - Has no relationship with insurer’s past experience Methods of calculation Retrospective method Looks at policy’s past premiums and benefits to determine reserves Reserve = accumulated value of – accumulated cost net premiums of insurance Group approach - Reserve arises from payment of level net premiums in excess of that need to meet current mortality costs - Premiums in early years are more than sufficient to pay death claims - Create a fund that can be used in later years, when death rates rise Individual approach - retrospective terminal reserve for any individual policy can be obtained too Cost of insurance - the contribution each insured must make as his share of death claims Prospective reserve Reserve = present value of -- present value of expected expected future benefits future net premiums * The two methods yield the same results Terminal, Initial, Mean reserves Classification depends on the point of time within the policy year when valuation occurs Terminal reserve - at the end of any given policy year - used in connection with dividend distributions - used to determine non-forfeiture values Initial reserve - at the beginning of policy year (is equal to the terminal reserve of the previous year) - used as the basis for allocation of interest earnings that exceed those assumed in the reserve Mean reserve - average of initial reserve and terminal reserve - used in connection with annual statements of life insurance companies Significance of actuarial assumptions - In measuring liabilities, life insurance company must make assumptions (rate of mortality, rate of earnings on the assets) - Different countries use different assumptions - The mortality tables and interest tables used have an impact on reserves Mortality - impossible to determine which mortality table will result in larger reserves - change in mortality affects number of deaths, and number of survivors - impact of a change is not uniform from age to age and duration to duration - may result in either increase or decrease Interest - if the rate if interest is decreased, there will be increase in reserves  smaller anticipated earnings must be offset by a larger reserve - the higher the interest rate used, the lower the present value Lapse or withdrawal rates - Statutory policy reserves are calculated based on assumption that no policies will withdraw from coverage (lapse) - Present value of future benefits is much greater than insurer’s actual present value of future benefits (… what?) Plan of insurance - All limited payment policies have the same reserves after they are paid up - After all premiums have been paid: o temporary life annuity due becomes 0 o reserve becomes net single premium at the insured’s attained age Modified Reserves - Ideally, each class of policies should pay its own cost - From insurer’s standpoint, the problem of meeting the expense as it occurs is more important - Primary difficulty: expenses of first policy year exceed those of any other year, and usually exceed the entire premium (agents’ first year commissions, expenses of physical examinations, approving applications, etc.) - Major problem: policies cannot pay first year expenses with amount available from first premium  expenses must be met immediately, but insurer must constantly: 1) maintain reasonable premium level, 2) pay death claims, 3) maintain standard reserve amount Surplus strain - Is an estimate of how much capital is necessary to finance new business - Particularly severe when a small company increases business rapidly - To fix, for a well-established insurer: o Pay expenses of new business from surplus, and replace the amount in the loadings of later premiums o Reducing policy reserve of first few yea
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