A2barx                  Second moment of continuous whole life
                        insurance PV
A2barxn                 Second moment of continuous endowment insurance
                        PV
A2barxn1                Second moment of continuous term insurance PV
A2nAbarx                Second moment of continuous deferred insurance
                        PV
A2nAx                   Second moment of deferred insurance PV
A2nAx_m                 Second moment of m-thly deferred insurance PV
A2nEx                   Second moment of pure endowment PV
A2x                     Second moment of whole life insurance PV
A2x_m                   Second moment of m-thly whole life insurance PV
A2xn                    Second moment of endowment insurance PV
A2xn1                   Second moment of term insurance PV
A2xn1_m                 Second moment of m-thly term insurance PV
A2xn_m                  Second moment of m-thly endowment insurance PV
AAL_PUC_db              Projected Unit Credit accrued liability
AAL_TUC_db              Traditional Unit Credit accrued liability
AB_cae                  Accrued benefit under a career-average-earnings
                        plan
AB_fas                  Accrued benefit under a final-average-salary
                        plan
APV_NR_db               Actuarial present value of a normal retirement
                        benefit
APV_gross_premiums      Actuarial present value of gross premiums
AS_path                 Projected asset-share path for two decrement
                        causes
AS_path_md              General projected asset-share path
AV_path_ul_typeA        Type A universal life account-value path
AV_path_ul_typeB        Type B universal life account-value path
AVz_dc                  Accumulated value of defined contribution plan
                        contributions
Abarx                   Continuous whole life insurance APV
Abarx_udd               UDD approximation of continuous whole life
                        insurance
Abarxj_md               Continuous multiple-decrement insurance present
                        value
Abarxn                  Continuous endowment insurance APV
Abarxn1                 Continuous term insurance APV
Abarxn1_udd             UDD approximation of continuous term insurance
Abarxn_udd              UDD approximation of continuous endowment
                        insurance
Ax                      Whole life insurance APV
Ax_m                    m-thly whole life insurance APV
Ax_m_udd                UDD approximation of m-thly whole life
                        insurance
Axj_md                  Discrete multiple-decrement insurance present
                        value
Axn                     Endowment insurance APV
Axn1                    Term insurance APV
Axn1_m                  m-thly term insurance APV
Axn1_m_udd              UDD approximation of m-thly term insurance
Axn_m                   m-thly endowment insurance APV
Axn_m_udd               UDD approximation of m-thly endowment insurance
DAbarxn1                Piecewise-continuous decreasing n-year term
                        insurance
DAxn1                   Decreasing n-year term insurance
DbarAbarxn1             Fully continuous decreasing n-year term
                        insurance
ELtx                    Mean present value of loss at duration t for
                        whole life insurance
GI_cont                 Interest gain for a continuous-style recursion
GI_disc                 Interest gain for a discrete insurance contract
GMF_rollforward_ul      Guaranteed maturity fund roll-forward
GM_cont                 Mortality gain for a continuous-style recursion
GM_disc                 Mortality gain for a discrete insurance
                        contract
GT_cont                 Total gain for a continuous-style one-step
                        recursion
GT_disc                 Total gain for a discrete insurance contract
GTg_disc                Total gross gain for a discrete insurance
                        contract
IAbarx                  Piecewise-continuous increasing whole life
                        insurance
IAx                     Increasing whole life insurance
IAxn1                   Increasing n-year term insurance
IRR_profit              Internal rate of return
IbarAbarx               Fully continuous increasing whole life
                        insurance
IbarAbarxn1             Fully continuous increasing n-year term
                        insurance
Income_dc               Retirement income from a defined contribution
                        accumulation
NC_EAN_db               Entry Age Normal normal cost
NC_PUC_db               Projected Unit Credit normal cost
NC_TUC_db               Traditional Unit Credit normal cost
NPV_partial             Partial net present values
NPV_profit              Net present value of a profit signature
PAB_cae                 Projected annual benefit under a
                        career-average-earnings plan
PAB_fas                 Projected annual benefit under a
                        final-average-salary plan
Pbar_trapz_ms           Continuous premium approximation in a
                        disability model
Pi_signature            Profit signature
PnAdotx                 Net premium for a deferred annuity-due
Pnax                    Net premium for a deferred annuity-immediate
Pr_vector_disc          Profit vector for a discrete profit-analysis
                        model
S0                      Survival function for age-at-failure
S0_to_lx                Convert survival probabilities to life-table
                        values
V_zeroized              Zeroized reserves for a discrete death-benefit
                        contract
Vprefloor_crvm_ul       Pre-floor CRVM reserve
ag38_prefunding_ratio   AG 38 prefunding ratio
ag38_reserve_ul         AG 38 reserve calculation
annuity_annual          Annual annuity functions
annuity_approximations_udd
                        UDD annuity approximations
annuity_approximations_woolhouse2
                        Woolhouse 2-term annuity approximations
annuity_approximations_woolhouse3
                        Woolhouse 3-term annuity approximations
annuity_certain         Present value of a level annuity-certain
annuity_mthly           m-thly contingent annuity functions
annuity_relationships   Annuity-insurance relationships
annuity_varying_payments
                        Varying-payment annuity functions
coi_ul_typeB            Cost of insurance for Type B universal life
continuous_multilife_annuities
                        Continuous multi-life annuities
continuous_multilife_insurance
                        Continuous multi-life insurance
contribution_rate_target
                        Target contribution rate for a defined
                        contribution plan
cov_term_deferred       Covariance of term and deferred insurance PVs
cov_term_endow          Covariance of term insurance and pure endowment
                        PVs
cumhaz0                 Cumulative hazard for age-at-failure
decompGg_disc           Ordered decomposition of gross gain
deferred_insurance_reserves
                        Deferred insurance reserves
discount                Discount factor for compound interest
discounted_payback_period
                        Discounted payback period
dist0                   Distribution functions for age-at-failure
double_force_delta      Doubled force of interest
double_force_i          Effective annual interest at doubled force
dx                      Compute deaths between ages x and x+1
dxj                     Cause-specific numbers of decrements
dxtau                   Total number of decrements
ex_complete             Complete expectation of life
ex_complete_tab         Complete expectation of life from a life table
ex_curtate              Curtate expectation of life
ex_curtate_tab          Curtate expectation of life from a life table
ex_temp_complete_tab    Temporary complete expectation of life from a
                        life table
ex_temp_curtate_tab     Temporary curtate expectation of life from a
                        life table
fnk_from_z              Forward rate implied by spot rates
forward_matrix_from_z   Matrix of forward rates implied by spot rates
fractional_duration_reserves
                        Fractional-duration whole life reserves
fractional_duration_term_endowment_reserves
                        Fractional-duration term and endowment reserves
full_preliminary_term   Full preliminary term modified premiums and
                        reserves
fx                      Conditional density
fx_tab                  Fractional conditional density from a life
                        table
gain_loss_md            Gain or loss in a two-cause multiple-decrement
                        model
gross_premium_expense_reserves
                        Whole life gross premium and expense reserves
hazard0                 Hazard or force of mortality for age-at-failure
htVx                    h-pay whole life net level premium reserve
iMA_eiul                Monthly-average index growth rate
iP_eiul                 Point-to-point index growth rates
i_credit_eiul           Credited rates from index growth rates
interest_convert        Convert between compound-interest quantities
joint_life_annuities    Joint-life annuities
joint_life_insurance    Joint-life insurance functions
last_survivor_annuities
                        Last-survivor annuity functions
last_survivor_insurance
                        Last-survivor insurance functions
life_table              Construct a life table
lx                      Extract life-table survivor values
lx_select               Extract select-table survivor value
lx_to_S0                Convert life-table values to survival
                        probabilities
markov_nstep_prob       Multi-step transition probability
md_table                Construct a multiple-decrement table
mortality_improvement_projection
                        Mortality improvement projection functions
multilife_contingent_probabilities
                        Contingent multi-life probabilities
multilife_pure_endowments
                        Multi-life pure endowments
multilife_survival_probabilities
                        Multi-life survival and failure probabilities
mux_tab                 Fractional force of mortality from a life table
nAbarx                  Continuous deferred insurance APV
nAbarx_udd              UDD approximation of continuous deferred
                        insurance
nAx                     Deferred insurance APV
nAx_m                   m-thly deferred insurance APV
nAx_m_udd               UDD approximation of m-thly deferred insurance
nEx                     Pure endowment APV
ndx                     Compute deaths over an n-year interval from a
                        life table
nkqx                    Curtate death probability from a life table
nmxq                    Deferred death probability from a life table
nmxq_select             Deferred select-life death probability
npx                     Compute n-year survival probability from a life
                        table
npx_select              Select-life survival probability
npxtau_md               Multiple-decrement survival probability from a
                        table
nqx                     Compute n-year death probability from a life
                        table
nqx_select              Select-life death probability
nqxj_md                 Cause-specific multiple-decrement probability
                        from a table
nqxtau_md               Total multiple-decrement probability from a
                        table
premium_functions       Premium, loss, and expense functions
profit_margin           Profit margin
pv_cashflows            Present value of cash flows at time 0
pv_spot_cashflows       Present value of deterministic cash flows using
                        spot rates
px_to_lx                Construct life-table values from p_x values
pxtau                   Total one-year survival probability
pxtau_ul                Universal life persistency probabilities
qx_dep_cf               Multiple-decrement probabilities under constant
                        forces
qx_dep_sudd             Multiple-decrement probabilities under SUDD
qx_tab                  Compute one-year death probability from a life
                        table
qx_to_lx                Construct life-table values from q_x values
qxprime_mudd            Associated single-decrement probabilities under
                        MUDD
qxprime_sudd            Associated single-decrement probabilities under
                        SUDD
qxtau                   Total one-year decrement probability
replacement_ratio_db    Replacement ratio for a defined benefit plan
replacement_ratio_dc    Replacement ratio for a defined contribution
                        plan
reversionary_annuities
                        Reversionary annuity functions
rt_ul                   Account-value to guaranteed-fund ratio
salary_scale            Salary scale under constant annual growth
select_life_table       Construct a select life table
solve_yield             Solve the yield rate by the equation of value
spot_interest_apvs      Actuarial present values under spot rates
tVbarAbarx              Fully continuous whole life reserve
tVbarx                  Whole life reserve with continuous premiums
tVnAdotx                Reserve for a deferred annuity-due
tVnEx                   Pure endowment net level premium reserve
tVnax                   Reserve for a deferred annuity-immediate
tVx                     Whole life net level premium reserve
tVx_m                   Whole life reserve with m-thly premiums
tVx_ret                 Retrospective whole life reserve
tVxn                    Endowment insurance net level premium reserve
tVxn1                   Term insurance net level premium reserve
tVxn1_ret               Retrospective term insurance reserve
tVxn_ret                Retrospective endowment insurance reserve
thiele_backward_path    Backward reserve path from a terminal value
thiele_backward_step    One backward numerical step for Thiele's
                        equation
thiele_dVdt             Reserve derivative from Thiele's equation
thiele_dVdt_01          Reserve derivatives for a disability model with
                        recovery
thiele_path_01          Backward reserve path for a disability model
                        with recovery
tp00_tp01_euler         Euler approximation of disability-state
                        probabilities
tpx                     Conditional survival probability
tpx_tab                 Fractional survival probability from a life
                        table
tpx_tau_cf              Total survival under constant cause-specific
                        forces
tpxprimej_cf            Single-decrement survival under a constant
                        force
tqx                     Conditional failure probability
tqx_tab                 Fractional failure probability from a life
                        table
tqxj_cf                 Cause-specific decrement probability under
                        constant forces
tqxprime_mudd           Fractional-year associated single-decrement
                        probabilities under MUDD
tqxprimej_cf            Single-decrement failure under a constant force
udd_continuous_multiplier
                        UDD multiplier for continuous insurance
                        approximations
udd_mthly_multiplier    UDD multiplier for m-thly insurance
                        approximations
varLtx                  Variance of present value of loss at duration t
                        for whole life insurance
var_Abarx               Variance of continuous whole life insurance PV
var_Abarxn              Variance of continuous endowment insurance PV
var_Abarxn1             Variance of continuous term insurance PV
var_Ax                  Variance of whole life insurance PV
var_Ax_m                Variance of m-thly whole life insurance PV
var_Axn                 Variance of endowment insurance PV
var_Axn1                Variance of term insurance PV
var_Axn1_m              Variance of m-thly term insurance PV
var_Axn_m               Variance of m-thly endowment insurance PV
var_nAbarx              Variance of continuous deferred insurance PV
var_nAx                 Variance of deferred insurance PV
var_nAx_m               Variance of m-thly deferred insurance PV
var_nEx                 Variance of pure endowment PV
variable_interest_apvs
                        Actuarial present values under variable annual
                        interest rates
vt_var                  Discount factors under variable annual interest
                        rates
z_from_coupon_annual    Bootstrap annual effective spot rates
z_from_coupon_semi      Bootstrap semiannual nominal spot rates
z_from_fn1              Spot rates from one-year forward rates
