- insurers limit coverage at older ages
- dis rates increase dramatically at older ages
- hard to tell between dis and normal ret at older ages

- Calc of PV of benefits is a 2-step process
- benefit provided at point of where dis occurs must be calced
- benefit is a disabled life annuity = PV waived prems using int and rates of termination of dis

- PV @ issue of each benefit is calces using int, active life mort and rates of dis
- calced at each point dis can occur and summed

- benefit provided at point of where dis occurs must be calced
- calc of actual gross prem can be simplified by loading published valn net prem
- loading determined by fitting adjusted experience prems to valn net prems

- Prems Waived
- prems used in benefit calc s/b net cost to insurer of prems actually waived
- consider
- commissions paid on waived prems
- prem taxes not paid on waived prems
- if offered, sex-distinct prems s/b used
- if prems vary by size of policy, either
- avg size s/b used or
- sep prems calced for each band

- YRT - S&U - simplified by calcing single AA table based on ultimates
- Term Conversions - should use permanent plan's premium in calc
- if prems vary by s/ns - blended rates or sep prems

- Interest
- significant impact b/c long dur benefit
- conservative LT rate s/b used

- Expenses
- cost of initial and ongoing claims investigation
- acctg for waived prems
- reserving for coverage
- command prem tax on premium for benefit
- some cos charge share of overhead

- Active Life Mortality
- used to determine survivorship for non-disabled lives for
- PV (@ issue) of benefits
- annuities used to calc net ann prem

- use same experience assumption used for pricing base coverage
- table of commutation functions D([x]+k) = v^(x+k)*l([x]+k)

- used to determine survivorship for non-disabled lives for
- Lapse Rates
- conservative to assume no lapses
- use base contract rates if using any

- Morbidity
- Rates of Disablement - measure chance of life aged (x) becoming disabled at age (x+k) (and remaining alive and disabled to end of waiting period)
- probability of disablement - r(x+k)
- absolute annual rate of disablement - r'(x+k)

- Rates of Termination of Disability
- needed to calc dis life annuity values
- measure probability of leaving the group of disabled lives (from recovery or death)
- highly select by duration since disablement
- usually monthly for first 2 years

- very few people beyond retirement age recover from disabled status
- Termination rates used to construct table for dis lives
- l_i([x+k]+m/12+s)
- k+1 - year disablement occurs
- m - months in waiting period
- s - duratoin since end of waiting period

- D_i([x+k]+m/12+s) = v^(x+k+m/12+s)*l_i([x+k]+m/12+s)

- Rates of Disablement - measure chance of life aged (x) becoming disabled at age (x+k) (and remaining alive and disabled to end of waiting period)

- Assume
- disabilities occur mid policy year
- prem and benefit payments payable continuously throughout policy year
- waiting period is 6 months

- B(k+1) - benefit provided if dis occurs in year k+1
- P(k) - prem/14m payable during k+1
- u = age wvr benefits end
- h - prem paying period of base plan
- n - cvoerage period for waiver provisoin = min(h,u-x)
- h' - prem paying period for waiver provision
- B(k+1) = sum(P(k+s+1)*(D_bar_i([x+k+1/2]+1/2+s) / D([x+k+1/2]+1/2))) from s=0 to n-k-2
- if P is level = P*abar_i([x+k+1/2]+1/2:n-k-1|)

- if coverage retroactive, B(k+1) increased by half prem payable in k+1 (0.5*P(k))
- PVB = B(k+1)*v^(x+k+1)*l([x]+k+1/2*r'(x+k) / D([x])
- = B(k+1)*v^(1/2)*r'(x+k)*D([x]+k+1/2) / D([x])

- NWSP = sum(PVB) from k = 0 to n-1 -> net waiver single premium
- NAWP = NWSP / active life annuity
- = sum(B(k+1)*v^(1/2)*r'(x+k)*D([x]+k+1/2)) / sum(D_bar([x]+k)) for (numerator) k = 0 to n-1 and (den) k=0 to h'-1

- To load for expenses
- E_wp(pi) - exp prem, loaded for expenses
- B'(k+1) - expense loaded benefit if dis in k+1
- c(k) = active life % prem expense in k+1
- e(i) - active life per pol expense in k+1
- c_i(s+1) - dis life % benefit expenses paying in dis year s+1
- e_i(s+1) - dis life per pol expense in s+1
- assuming per pol expenses paid @ BOY and % expenses paid continuously
- B'(k+1) = .5*P(k) + sum{[P(k+s+1)*(1+c_i(s+1)) + e_i(s+1)]*[D_bar_i([x+k+1/2]+1/2+s)/D_bar_i([x+k+1/2])]} for s = 0 to n-k-2
- E_wp(pi) = sum{[e(k)*D([x]+k) + B'(k+1)*v^(1/2)*r'(x+k)*D([x]+k+1/2)]} / sum{(1-c(k))*D_bar([x]+k)} for (num) k=0 to n-1 and (den) k=0 to h'-1

- substandard risks
- waiver usually restricted to least substd risks
- waiver prems usually multiples of std business wvr prems

- Payor Benefit
- waives premiums if payor of juvenile policy is death/dis until juv attaines 21/25
- prems depend on age of applicant, plan of ins, age of insured
- gross prems usually published at table of factors

- Riders on Insured Spouse or Children
- waives rider prems
- based on base insured, not spouse or children

- Non-traditional Products
- indeterminate prem products
- using guar prems in calc is conservative
- might be uncompetitive

- use judgement re: most likely scale of prems to be charged and use in calcs

- using guar prems in calc is conservative
- UL
- waiver of coi
- specified amt - use specified amt in formulas and is aount req'd to keep contract in force if all guarantees realized
- does not have any relationship to prms actually paid into contract

- either case, use same formulas, just different P(k) stream

- indeterminate prem products

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