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 for a
                        DB plan
AAL_TUC_db              Traditional Unit Credit accrued liability for a
                        DB plan
AB_cae                  Accrued benefit for a career average earnings
                        plan
AB_fas                  Accrued benefit for a final average salary plan
APV_NR_db               APV of normal retirement benefit for a DB plan
APV_gross_premiums      APV of gross premiums under a risk discount
                        rate
AS_path                 Projected asset share path {}_{k}AS
AS_path_md              General projected asset share path (multiple
                        decrements)
AV_path_ul_typeA        Account-value path for Type A universal life
AV_path_ul_typeB        Account-value path for Type B universal life
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 APV
                        \overline{A}_{x}^{(j)}
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
Abarxy                  Continuous joint-life whole life insurance
Abarxy1                 Continuous contingent insurance: benefit on
                        death of (x) if before (y)
Abarxy2                 Continuous contingent insurance: benefit on
                        death of (x) if after (y)
Abarxybar               Continuous last-survivor whole life insurance
Abaryx1                 Continuous contingent insurance: benefit on
                        death of (y) if before (x)
Abaryx2                 Continuous contingent insurance: benefit on
                        death of (y) if after (x)
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 APV
                        A_{x}^{(j)}
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
Axy                     Joint-life whole life insurance
Axybar                  Last-survivor whole life insurance
Axybarn                 Last-survivor endowment insurance
Axybarn1                Last-survivor term insurance
Axyn                    Joint-life endowment insurance
Axyn1                   Joint-life term 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 helper for continuous-style
                        recursion
GI_disc                 Interest gain for a discrete insurance contract
GMF_rollforward_ul      Guaranteed maturity fund roll-forward
GM_cont                 Mortality gain helper for 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 of a profit signature
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 for a DB plan
NC_PUC_db               Projected Unit Credit normal cost for a DB plan
NC_TUC_db               Traditional Unit Credit normal cost for a DB
                        plan
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 DB plan
PAB_fas                 Projected annual benefit under a final average
                        salary DB plan
Pbar_trapz_ms           Continuous premium approximation \overline{P}
                        by trapezoidal rule
Pi_signature            Profit signature from a profit vector
PnAdotx                 Deferred annuity-due premium
Pnax                    Deferred annuity-immediate premium
Pr_vector_disc          Profit vector for a discrete profit-analysis
                        model
S0                      Survival function for age-at-failure T0
S0_to_lx                Convert survival probabilities to life-table
                        values
V_zeroized              Zeroized reserves for a discrete death-only
                        contract
Vprefloor_crvm_ul       Pre-floor CRVM reserve for universal life
abarx_y                 Continuous reversionary annuity to (y) after
                        death of (x)
abarxy_ch12             Continuous joint-life whole life annuity
abarxybar_ch12          Continuous last-survivor whole life annuity
abary_x                 Continuous reversionary annuity to (x) after
                        death of (y)
adotxy                  Joint-life whole life annuity-due
adotxybar               Last-survivor whole life annuity-due
adotxybarn              Last-survivor temporary annuity-due
adotxyn                 Joint-life temporary annuity-due
ag38_prefunding_ratio   AG 38 prefunding ratio
ag38_reserve_ul         AG 38 reserve calculation
alphaF                  Full preliminary term first-year modified
                        premium
annuity_annual          Annual annuity functions (Chapter 8)
annuity_approximations
                        Annuity approximations (Chapter 8)
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 (Chapter 8)
annuity_mthly_accum_due
                        Temporary m-thly annuity-due actuarial
                        accumulated value
annuity_mthly_accum_immediate
                        Temporary m-thly annuity-immediate actuarial
                        accumulated value
annuity_mthly_deferred_due
                        Deferred whole life m-thly annuity-due
annuity_mthly_deferred_immediate
                        Deferred whole life m-thly annuity-immediate
annuity_mthly_temp_due
                        Temporary m-thly annuity-due
annuity_mthly_temp_immediate
                        Temporary m-thly annuity-immediate
annuity_mthly_whole_due
                        Whole life m-thly annuity-due
annuity_mthly_whole_immediate
                        Whole life m-thly annuity-immediate
annuity_relationships   Annuity-insurance relationships (Chapter 8)
annuity_varying_payments
                        Varying-payment annuity functions (Chapter 8)
ax_improved             Whole life annuity-immediate under mortality
                        improvement
ax_y                    Reversionary annuity to (y) after death of (x)
axn_improved            Temporary annuity-immediate under mortality
                        improvement
axy_ch12                Joint-life whole life annuity-immediate
axybar_ch12             Last-survivor whole life annuity-immediate
axybarn_ch12            Last-survivor temporary annuity-immediate
axyn_ch12               Joint-life temporary annuity-immediate
ay_x                    Reversionary annuity to (x) after death of (y)
betaF                   Full preliminary term renewal modified premium
ch12_multilife_cont_params
                        Shared parameters for Chapter 12 continuous
                        multi-life functions
chapter15_spot_interest_apv
                        Spot-rate actuarial present value functions
chapter15_variable_interest_apv
                        Variable-interest actuarial present value
                        functions
coi_ul_typeB            Cost of insurance for Type B universal life
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 T0
decompGg_disc           Ordered gross gain decomposition
discount                Discount factor for compound interest
discounted_payback_period
                        Discounted payback period
dist0                   Distribution functions for age-at-failure T0
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 decrements d_x^{(j)}
dxtau                   Total decrements d_x^{(tau)}
ex_complete             Complete expectation of life at age x
ex_complete_tab         Complete expectation of life from a life table
ex_curtate              Curtate expectation of life at age x
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 f_{n,k} from spot rates
forward_matrix_from_z   Matrix of all determinable forward rates from
                        spot rates
fx                      Conditional density for Tx
fx_tab                  Fractional conditional density from a life
                        table
gain_loss_md            Gain or loss in a multiple-decrement model
hazard0                 Hazard / force for age-at-failure T0
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 raw index growth rates
interest_convert        Convert between compound-interest quantities
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       n-step transition probability for a
                        discrete-time Markov chain
md_table                Build a multiple-decrement table
meanVx                  Mean reserve for whole life insurance
mortality_improvement   Mortality improvement projection functions
                        (Chapter 8)
multilife_ch12          Multi-life functions for Chapter 12
multilife_ch12_ext      Extended multi-life functions for Chapter 12
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
nExy                    Joint-life pure endowment
nExybar                 Last-survivor pure endowment
naxn_improved           Deferred temporary annuity-immediate under
                        mortality improvement
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               {}_n p_x^{(tau)} from a multiple-decrement
                        table
nqx                     Compute n-year death probability from a life
                        table
nqx_select              Select-life death probability
nqxj_md                 {}_n q_x^{(j)} from a multiple-decrement table
nqxtau_md               {}_n q_x^{(tau)} from a multiple-decrement
                        table
premium_ch9             Chapter 9 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 cash flows using spot rates
px_proj                 Project one-year survival probability under
                        mortality improvement
px_to_lx                Construct life-table values from p_x values
pxtau                   Survival probability p_x^{(tau)}
pxtau_ul                One-year persistency rates for universal life
qx_dep_cf               Dependent probabilities q_x^{(j)} from
                        independent probabilities q_x^{\prime(j)} under
                        constant force
qx_dep_sudd             Dependent probabilities q_x^{(j)} from
                        independent probabilities q_x^{\prime(j)} under
                        SUDD
qx_proj                 Project one-year death probability under
                        mortality improvement
qx_tab                  Compute one-year death probability from a life
                        table
qx_to_lx                Construct life-table values from q_x values
qxprime_mudd            Independent probabilities q_x^{\prime(j)} from
                        dependent probabilities q_x^{(j)} under MUDD
qxprime_sudd            Independent probabilities q_x^{\prime(j)} from
                        dependent probabilities q_x^{(j)} under SUDD
qxtau                   Total probability of decrement q_x^{(tau)}
replacement_ratio_db    Replacement ratio for a defined benefit plan
replacement_ratio_dc    Replacement ratio for a defined contribution
                        plan
reserve_ch10            Reserve functions for Chapter 10
reserve_ch10_ext        Extended reserve functions for Chapter 10
reserve_ch11            Reserve functions for Chapter 11
reserve_ch11_ext        Extended reserve functions for Chapter 11
reserve_deferred_insurance_ch10
                        Deferred insurance reserve functions
rt_ul                   Ratio r_t = AV_t / GMF_t capped at 1
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
tVEx                    Whole life expense reserve
tVFx                    Full preliminary term reserve for whole life
                        insurance
tVGx                    Whole life gross premium reserve
tVbarAbarx              Fully continuous whole life reserve
tVbarx                  Whole life reserve with continuous premiums
tVnAdotx                Deferred annuity-due reserve
tVnEx                   Pure endowment net level premium reserve
tVnax                   Deferred annuity-immediate reserve
tVx                     Whole life net level premium reserve
tVx_m                   Whole life reserve with m-thly premiums
tVx_ret                 Whole life net level premium reserve by
                        retrospective method
tVxn                    Endowment insurance net level premium reserve
tVxn1                   Term insurance net level premium reserve
tVxn1_ret               Term insurance reserve by retrospective method
tVxn_ret                Endowment insurance reserve by retrospective
                        method
thiele_backward_path    Backward Euler reserve path from maturity
thiele_backward_step    One backward Euler-style Thiele step
thiele_dVdt             Reserve derivative from Thiele's equation
thiele_dVdt_01          Reserve derivatives for the disability model
                        with recovery
thiele_path_01          Backward reserve path for the disability model
                        with recovery
tp00_tp01_euler         Euler approximation for {}_{t}p_{x}^{00} and
                        {}_{t}p_{x}^{01}
tpx                     Conditional survival probability for Tx
tpx_improved            Multi-year survival probability under mortality
                        improvement
tpx_tab                 Fractional survival probability from a life
                        table
tpx_tau_cf              Total survival probability {}_t p_x^{(tau)}
                        under constant forces
tpxprimej_cf            Single-decrement survival probability {}_t
                        p_x^{\prime(j)} under constant force
tpxtau_ul               Cumulative persistency to the end of each
                        policy year
tpxy                    Joint-life survival probability
tpxybar                 Last-survivor survival probability
tqx                     Conditional failure probability for Tx
tqx_tab                 Fractional failure probability from a life
                        table
tqxj_cf                 Cause-specific probability {}_t q_x^{(j)} under
                        constant forces
tqxprime_mudd           Independent probabilities {}_t q_x^{\prime(j)}
                        under MUDD
tqxprimej_cf            Single-decrement failure probability {}_t
                        q_x^{\prime(j)} under constant force
tqxy                    Joint-life failure probability
tqxy1                   Probability that (x) fails before (y) within n
                        years
tqxy2                   Probability that (x) fails after (y) within n
                        years
tqxybar                 Last-survivor failure probability
tqyx1                   Probability that (y) fails before (x) within n
                        years
tqyx2                   Probability that (y) fails after (x) within n
                        years
tsVx                    Fractional-duration whole life reserve
tsVxn                   Fractional-duration endowment reserve
tsVxn1                  Fractional-duration term reserve
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
vt_var                  Discount factors under a variable annual
                        interest scenario
z_from_coupon_annual    Bootstrap annual spot rates from annual
                        coupon-bond yields
z_from_coupon_semi      Bootstrap semiannual nominal spot rates from
                        coupon-bond yields
z_from_fn1              Spot rates from forward one-year rates
