# Actuarial Risk Modeling and Life Contingencies

## Documentation for package ‘mqriskR’ version 0.1.1

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

A B C D E F G H I J L M N P Q R S T U V Z

## -- A --

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
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
A2x_m | Second moment of m-thly whole life insurance PV
AAL_PUC_db | Projected Unit Credit accrued liability
AAL_TUC_db | Traditional Unit Credit accrued liability
Abarx | Continuous whole life insurance APV
abarx | Annual annuity functions
Abarxj_md | Continuous multiple-decrement insurance present value
Abarxn | Continuous endowment insurance APV
abarxn | Annual annuity functions
Abarxn1 | Continuous term insurance APV
Abarxn1_udd | UDD approximation of continuous term insurance
Abarxn_udd | UDD approximation of continuous endowment insurance
abarxn_udd | UDD annuity approximations
Abarxy | Continuous multi-life insurance
abarxy | Continuous multi-life annuities
Abarxy1 | Continuous multi-life insurance
Abarxy2 | Continuous multi-life insurance
Abarxybar | Continuous multi-life insurance
abarxybar | Continuous multi-life annuities
Abarx_udd | UDD approximation of continuous whole life insurance
abarx_udd | UDD annuity approximations
abarx_woolhouse2 | Woolhouse 2-term annuity approximations
abarx_woolhouse3 | Woolhouse 3-term annuity approximations
abarx_y | Continuous multi-life annuities
Abaryx1 | Continuous multi-life insurance
Abaryx2 | Continuous multi-life insurance
abary_x | Continuous multi-life annuities
AB_cae | Accrued benefit under a career-average-earnings plan
AB_fas | Accrued benefit under a final-average-salary plan
adotx | Annual annuity functions
adotxn | Annual annuity functions
adotxn_m | m-thly contingent annuity functions
adotxn_m_udd | UDD annuity approximations
adotxn_m_woolhouse2 | Woolhouse 2-term annuity approximations
adotxn_m_woolhouse3 | Woolhouse 3-term annuity approximations
adotxy | Joint-life annuities
adotxybar | Last-survivor annuity functions
adotxybarn | Last-survivor annuity functions
adotxyn | Joint-life annuities
adotx_m | m-thly contingent annuity functions
adotx_m_udd | UDD annuity approximations
adotx_m_woolhouse2 | Woolhouse 2-term annuity approximations
adotx_m_woolhouse3 | Woolhouse 3-term annuity approximations
ag38_prefunding_ratio | AG 38 prefunding ratio
ag38_reserve_ul | AG 38 reserve calculation
alphaF | Full preliminary term modified premiums and reserves
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_identity_abarx | Annuity-insurance relationships
annuity_identity_abarxn | Annuity-insurance relationships
annuity_identity_adotx | Annuity-insurance relationships
annuity_identity_adotxn | Annuity-insurance relationships
annuity_identity_ax | Annuity-insurance relationships
annuity_identity_axn | Annuity-insurance relationships
annuity_identity_nabarx | Annuity-insurance relationships
annuity_identity_nadotx | Annuity-insurance relationships
annuity_identity_nax | Annuity-insurance relationships
annuity_mthly | m-thly contingent annuity functions
annuity_relationships | Annuity-insurance relationships
annuity_varying_payments | Varying-payment annuity functions
APV_gross_premiums | Actuarial present value of gross premiums
APV_NR_db | Actuarial present value of a normal retirement benefit
AS_path | Projected asset-share path for two decrement causes
AS_path_md | General projected asset-share path
AVz_dc | Accumulated value of defined contribution plan contributions
AV_path_ul_typeA | Type A universal life account-value path
AV_path_ul_typeB | Type B universal life account-value path
Ax | Whole life insurance APV
ax | Annual annuity functions
Axj_md | Discrete multiple-decrement insurance present value
Axn | Endowment insurance APV
axn | Annual annuity functions
Axn1 | Term insurance APV
Axn1_m | m-thly term insurance APV
Axn1_m_udd | UDD approximation of m-thly term insurance
Axn1_spot | Actuarial present values under spot rates
Axn1_var | Actuarial present values under variable annual interest rates
axn_improved | Mortality improvement projection functions
Axn_m | m-thly endowment insurance APV
axn_m | m-thly contingent annuity functions
Axn_m_udd | UDD approximation of m-thly endowment insurance
axn_m_udd | UDD annuity approximations
axn_m_woolhouse2 | Woolhouse 2-term annuity approximations
axn_m_woolhouse3 | Woolhouse 3-term annuity approximations
Axn_spot | Actuarial present values under spot rates
axn_spot | Actuarial present values under spot rates
Axn_var | Actuarial present values under variable annual interest rates
axn_var | Actuarial present values under variable annual interest rates
Axy | Joint-life insurance functions
axy | Joint-life annuities
Axybar | Last-survivor insurance functions
axybar | Last-survivor annuity functions
Axybarn | Last-survivor insurance functions
axybarn | Last-survivor annuity functions
Axybarn1 | Last-survivor insurance functions
Axyn | Joint-life insurance functions
axyn | Joint-life annuities
Axyn1 | Joint-life insurance functions
ax_improved | Mortality improvement projection functions
Ax_m | m-thly whole life insurance APV
ax_m | m-thly contingent annuity functions
Ax_m_udd | UDD approximation of m-thly whole life insurance
ax_m_udd | UDD annuity approximations
ax_m_woolhouse2 | Woolhouse 2-term annuity approximations
ax_m_woolhouse3 | Woolhouse 3-term annuity approximations
ax_y | Reversionary annuity functions
ay_x | Reversionary annuity functions

## -- B --

betaF | Full preliminary term modified premiums and reserves

## -- C --

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

## -- D --

Dabarxn | Varying-payment annuity functions
DAbarxn1 | Piecewise-continuous decreasing n-year term insurance
Dadotxn | Varying-payment annuity functions
Daxn | Varying-payment annuity functions
DAxn1 | Decreasing n-year term insurance
DbarAbarxn1 | Fully continuous decreasing n-year term insurance
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

## -- E --

EL0barAbarx | Premium, loss, and expense functions
EL0x | Premium, loss, and expense functions
EL0xn | Premium, loss, and expense functions
EL0xn1 | Premium, loss, and expense functions
ELtx | Mean present value of loss at duration t for whole life insurance
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

## -- F --

F0 | Distribution functions for age-at-failure
f0 | Distribution functions for age-at-failure
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

## -- G --

gain_loss_md | Gain or loss in a two-cause multiple-decrement model
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
gross_premium_expense_reserves | Whole life gross premium and expense reserves
GTg_disc | Total gross 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
Gx | Premium, loss, and expense functions

## -- H --

hazard0 | Hazard or force of mortality for age-at-failure
htVnAx | Deferred insurance reserves
htVx | h-pay whole life net level premium reserve

## -- I --

IAbarx | Piecewise-continuous increasing whole life insurance
Iabarx | Varying-payment annuity functions
Iabarxn | Varying-payment annuity functions
Iadotx | Varying-payment annuity functions
Iadotxn | Varying-payment annuity functions
IAx | Increasing whole life insurance
Iax | Varying-payment annuity functions
Iaxn | Varying-payment annuity functions
IAxn1 | Increasing n-year term insurance
IbarAbarx | Fully continuous increasing whole life insurance
IbarAbarxn1 | Fully continuous increasing n-year term insurance
iMA_eiul | Monthly-average index growth rate
Income_dc | Retirement income from a defined contribution accumulation
interest_convert | Convert between compound-interest quantities
iP_eiul | Point-to-point index growth rates
IRR_profit | Internal rate of return
i_credit_eiul | Credited rates from index growth rates

## -- J --

joint_life_annuities | Joint-life annuities
joint_life_insurance | Joint-life insurance functions

## -- L --

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

## -- M --

markov_nstep_prob | Multi-step transition probability
md_table | Construct a multiple-decrement table
meanVx | Fractional-duration whole life reserves
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

## -- N --

nAbarx | Continuous deferred insurance APV
nabarx | Annual annuity functions
nAbarx_udd | UDD approximation of continuous deferred insurance
nabarx_udd | UDD annuity approximations
nadotx | Annual annuity functions
nadotx_m | m-thly contingent annuity functions
nadotx_m_udd | UDD annuity approximations
nadotx_m_woolhouse2 | Woolhouse 2-term annuity approximations
nadotx_m_woolhouse3 | Woolhouse 3-term annuity approximations
nAx | Deferred insurance APV
nax | Annual annuity functions
naxn_improved | Mortality improvement projection functions
nAx_m | m-thly deferred insurance APV
nax_m | m-thly contingent annuity functions
nAx_m_udd | UDD approximation of m-thly deferred insurance
nax_m_udd | UDD annuity approximations
nax_m_woolhouse2 | Woolhouse 2-term annuity approximations
nax_m_woolhouse3 | Woolhouse 3-term annuity approximations
NC_EAN_db | Entry Age Normal normal cost
NC_PUC_db | Projected Unit Credit normal cost
NC_TUC_db | Traditional Unit Credit normal cost
ndx | Compute deaths over an n-year interval from a life table
nEx | Pure endowment APV
nExy | Multi-life pure endowments
nExybar | Multi-life pure endowments
nEx_spot | Actuarial present values under spot rates
nEx_var | Actuarial present values under variable annual interest rates
nkqx | Curtate death probability from a life table
nmxq | Deferred death probability from a life table
nmxq_select | Deferred select-life death probability
NPV_partial | Partial net present values
NPV_profit | Net present value of a profit signature
npx | Compute n-year survival probability from a life table
npxtau_md | Multiple-decrement survival probability from a table
npx_select | Select-life survival probability
nqx | Compute n-year death probability from a life table
nqxj_md | Cause-specific multiple-decrement probability from a table
nqxtau_md | Total multiple-decrement probability from a table
nqx_select | Select-life death probability

## -- P --

PAB_cae | Projected annual benefit under a career-average-earnings plan
PAB_fas | Projected annual benefit under a final-average-salary plan
PbarAbarx | Premium, loss, and expense functions
PbarAbarxn | Premium, loss, and expense functions
PbarAbarxn1 | Premium, loss, and expense functions
Pbarx | Premium, loss, and expense functions
Pbarxn | Premium, loss, and expense functions
Pbarxn1 | Premium, loss, and expense functions
Pbar_trapz_ms | Continuous premium approximation in a disability model
Pi_signature | Profit signature
PnAdotx | Net premium for a deferred annuity-due
PnAx | Premium, loss, and expense functions
Pnax | Net premium for a deferred annuity-immediate
PnAx_m | Premium, loss, and expense functions
PnEx | Premium, loss, and expense functions
premium_functions | Premium, loss, and expense functions
profit_margin | Profit margin
Pr_vector_disc | Profit vector for a discrete profit-analysis model
pv_cashflows | Present value of cash flows at time 0
pv_spot_cashflows | Present value of deterministic cash flows using spot rates
Px | Premium, loss, and expense functions
Pxn | Premium, loss, and expense functions
Pxn1 | Premium, loss, and expense functions
Pxn1_m | Premium, loss, and expense functions
Pxn_m | Premium, loss, and expense functions
pxtau | Total one-year survival probability
pxtau_ul | Universal life persistency probabilities
Px_m | Premium, loss, and expense functions
px_proj | Mortality improvement projection functions
px_to_lx | Construct life-table values from p_x values

## -- Q --

qxprime_mudd | Associated single-decrement probabilities under MUDD
qxprime_sudd | Associated single-decrement probabilities under SUDD
qxtau | Total one-year decrement probability
qx_dep_cf | Multiple-decrement probabilities under constant forces
qx_dep_sudd | Multiple-decrement probabilities under SUDD
qx_proj | Mortality improvement projection functions
qx_tab | Compute one-year death probability from a life table
qx_to_lx | Construct life-table values from q_x values

## -- R --

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

## -- S --

S0 | Survival function for age-at-failure
S0_to_lx | Convert survival probabilities to life-table values
salary_scale | Salary scale under constant annual growth
sbarxn | Annual annuity functions
sdotxn | Annual annuity functions
sdotxn_m | m-thly contingent annuity functions
sdotxn_m_udd | UDD annuity approximations
sdotxn_m_woolhouse2 | Woolhouse 2-term annuity approximations
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
sxn | Annual annuity functions
sxn_m | m-thly contingent annuity functions
sxn_m_udd | UDD annuity approximations
sxn_m_woolhouse2 | Woolhouse 2-term annuity approximations

## -- T --

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
tPnAx | Premium, loss, and expense functions
tPnEx | Premium, loss, and expense functions
tPx | Premium, loss, and expense functions
tpx | Conditional survival probability
tPxn | Premium, loss, and expense functions
tPxn1 | Premium, loss, and expense functions
tpxprimej_cf | Single-decrement survival under a constant force
tpxtau_ul | Universal life persistency probabilities
tpxy | Multi-life survival and failure probabilities
tpxybar | Multi-life survival and failure probabilities
tpx_improved | Mortality improvement projection functions
tpx_tab | Fractional survival probability from a life table
tpx_tau_cf | Total survival under constant cause-specific forces
tqx | Conditional failure probability
tqxj_cf | Cause-specific decrement probability under constant forces
tqxprimej_cf | Single-decrement failure under a constant force
tqxprime_mudd | Fractional-year associated single-decrement probabilities under MUDD
tqxy | Multi-life survival and failure probabilities
tqxy1 | Contingent multi-life probabilities
tqxy2 | Contingent multi-life probabilities
tqxybar | Multi-life survival and failure probabilities
tqx_tab | Fractional failure probability from a life table
tqyx1 | Contingent multi-life probabilities
tqyx2 | Contingent multi-life probabilities
tsVx | Fractional-duration whole life reserves
tsVxn | Fractional-duration term and endowment reserves
tsVxn1 | Fractional-duration term and endowment reserves
tVbarAbarx | Fully continuous whole life reserve
tVbarx | Whole life reserve with continuous premiums
tVEx | Whole life gross premium and expense reserves
tVFx | Full preliminary term modified premiums and reserves
tVGx | Whole life gross premium and expense reserves
tVnAdotx | Reserve for a deferred annuity-due
tVnAx | Deferred insurance reserves
tVnax | Reserve for a deferred annuity-immediate
tVnEx | Pure endowment net level premium reserve
tVx | Whole life net level premium 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
tVx_m | Whole life reserve with m-thly premiums
tVx_ret | Retrospective whole life reserve

## -- U --

udd_continuous_multiplier | UDD multiplier for continuous insurance approximations
udd_mthly_multiplier | UDD multiplier for m-thly insurance approximations

## -- V --

variable_interest_apvs | Actuarial present values under variable annual interest rates
varL0barAbarx | Premium, loss, and expense functions
varL0x | Premium, loss, and expense functions
varL0xn | Premium, loss, and expense functions
varL0xn1 | Premium, loss, and expense functions
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_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_Ax_m | Variance of m-thly whole life 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
Vprefloor_crvm_ul | Pre-floor CRVM reserve
vt_var | Discount factors under variable annual interest rates
V_zeroized | Zeroized reserves for a discrete death-benefit contract

## -- Z --

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