Package index • mqriskR

Interest Theory

interest_convert(): Convert between compound-interest quantities
discount(): Discount factor for compound interest
pv_cashflows(): Present value of cash flows at time 0
solve_yield(): Solve the yield rate by the equation of value
annuity_certain(): Present value of a level annuity-certain

Survival Models

S0(): Survival function for age-at-failure T0
F0() f0(): Distribution functions for age-at-failure T0
hazard0(): Hazard / force for age-at-failure T0
cumhaz0(): Cumulative hazard for age-at-failure T0
tpx(): Conditional survival probability for Tx
tqx(): Conditional failure probability for Tx
fx(): Conditional density for Tx
ex_complete(): Complete expectation of life at age x
ex_curtate(): Curtate expectation of life at age x

Life Tables

S0_to_lx(): Convert survival probabilities to life-table values
lx_to_S0(): Convert life-table values to survival probabilities
px_to_lx(): Construct life-table values from p_x values
qx_to_lx(): Construct life-table values from q_x values
life_table(): Construct a life table
lx(): Extract life-table survivor values
dx(): Compute deaths between ages x and x+1
ndx(): Compute deaths over an n-year interval from a life table
qx_tab(): Compute one-year death probability from a life table
npx(): Compute n-year survival probability from a life table
nqx(): Compute n-year death probability from a life table
select_life_table(): Construct a select life table
lx_select(): Extract select-table survivor value
npx_select(): Select-life survival probability
nqx_select(): Select-life death probability
nmxq_select(): Deferred select-life death probability
tpx_tab(): Fractional survival probability from a life table
tqx_tab(): Fractional failure probability from a life table
mux_tab(): Fractional force of mortality from a life table
fx_tab(): Fractional conditional density from a life table
nmxq(): Deferred death probability from a life table
nkqx(): Curtate death probability from a life table
ex_curtate_tab(): Curtate expectation of life from a life table
ex_temp_curtate_tab(): Temporary curtate expectation of life from a life table
ex_temp_complete_tab(): Temporary complete expectation of life from a life table
ex_complete_tab(): Complete expectation of life from a life table

Contingent Payment Models

double_force_i(): Effective annual interest at doubled force
double_force_delta(): Doubled force of interest
udd_continuous_multiplier(): UDD multiplier for continuous insurance approximations
udd_mthly_multiplier(): UDD multiplier for m-thly insurance approximations
Abarx_udd(): UDD approximation of continuous whole life insurance
Abarxn1_udd(): UDD approximation of continuous term insurance
nAbarx_udd(): UDD approximation of continuous deferred insurance
Abarxn_udd(): UDD approximation of continuous endowment insurance
Ax_m_udd(): UDD approximation of m-thly whole life insurance
Axn1_m_udd(): UDD approximation of m-thly term insurance
nAx_m_udd(): UDD approximation of m-thly deferred insurance
Axn_m_udd(): UDD approximation of m-thly endowment insurance
Ax(): Whole life insurance APV
Axn1(): Term insurance APV
nEx(): Pure endowment APV
nAx(): Deferred insurance APV
Axn(): Endowment insurance APV
A2x(): Second moment of whole life insurance PV
A2xn1(): Second moment of term insurance PV
A2nEx(): Second moment of pure endowment PV
A2nAx(): Second moment of deferred insurance PV
A2xn(): Second moment of endowment insurance PV
var_Ax(): Variance of whole life insurance PV
var_Axn1(): Variance of term insurance PV
var_nEx(): Variance of pure endowment PV
var_nAx(): Variance of deferred insurance PV
var_Axn(): Variance of endowment insurance PV
cov_term_deferred(): Covariance of term and deferred insurance PVs
cov_term_endow(): Covariance of term insurance and pure endowment PVs
Abarx(): Continuous whole life insurance APV
Abarxn1(): Continuous term insurance APV
nAbarx(): Continuous deferred insurance APV
Abarxn(): Continuous endowment insurance APV
A2barx(): Second moment of continuous whole life insurance PV
A2barxn1(): Second moment of continuous term insurance PV
A2nAbarx(): Second moment of continuous deferred insurance PV
A2barxn(): Second moment of continuous endowment insurance PV
var_Abarx(): Variance of continuous whole life insurance PV
var_Abarxn1(): Variance of continuous term insurance PV
var_nAbarx(): Variance of continuous deferred insurance PV
var_Abarxn(): Variance of continuous endowment insurance PV
Ax_m(): m-thly whole life insurance APV
Axn1_m(): m-thly term insurance APV
nAx_m(): m-thly deferred insurance APV
Axn_m(): m-thly endowment insurance APV
A2x_m(): Second moment of m-thly whole life insurance PV
A2xn1_m(): Second moment of m-thly term insurance PV
A2nAx_m(): Second moment of m-thly deferred insurance PV
A2xn_m(): Second moment of m-thly endowment insurance PV
var_Ax_m(): Variance of m-thly whole life insurance PV
var_Axn1_m(): Variance of m-thly term insurance PV
var_nAx_m(): Variance of m-thly deferred insurance PV
var_Axn_m(): Variance of m-thly endowment insurance PV
IAx(): Increasing whole life insurance
IAxn1(): Increasing n-year term insurance
DAxn1(): Decreasing n-year term insurance
IbarAbarx(): Fully continuous increasing whole life insurance
IAbarx(): Piecewise-continuous increasing whole life insurance
IbarAbarxn1(): Fully continuous increasing n-year term insurance
DbarAbarxn1(): Fully continuous decreasing n-year term insurance
DAbarxn1(): Piecewise-continuous decreasing n-year term insurance

Contingent Annuity Models

ax() adotx() abarx() axn() adotxn() abarxn() nax() nadotx() nabarx() sxn() sdotxn() sbarxn(): Annual annuity functions (Chapter 8)
ax_m(): Whole life m-thly annuity-immediate
adotx_m(): Whole life m-thly annuity-due
axn_m(): Temporary m-thly annuity-immediate
adotxn_m(): Temporary m-thly annuity-due
nax_m(): Deferred whole life m-thly annuity-immediate
nadotx_m(): Deferred whole life m-thly annuity-due
sxn_m(): Temporary m-thly annuity-immediate actuarial accumulated value
sdotxn_m(): Temporary m-thly annuity-due actuarial accumulated value
annuity_identity_ax() annuity_identity_adotx() annuity_identity_abarx() annuity_identity_axn() annuity_identity_adotxn() annuity_identity_abarxn() annuity_identity_nax() annuity_identity_nadotx() annuity_identity_nabarx(): Annuity-insurance relationships (Chapter 8)
Iax() Iaxn() Daxn() Iadotx() Iadotxn() Dadotxn() Iabarx() Iabarxn() Dabarxn(): Varying-payment annuity functions (Chapter 8)
qx_proj(): Project one-year death probability under mortality improvement
px_proj(): Project one-year survival probability under mortality improvement
tpx_improved(): Multi-year survival probability under mortality improvement
axn_improved(): Temporary annuity-immediate under mortality improvement
naxn_improved(): Deferred temporary annuity-immediate under mortality improvement
ax_improved(): Whole life annuity-immediate under mortality improvement
adotx_m_udd() adotxn_m_udd() nadotx_m_udd() ax_m_udd() axn_m_udd() nax_m_udd() sdotxn_m_udd() sxn_m_udd() abarx_udd() abarxn_udd() nabarx_udd(): UDD annuity approximations
ax_m_woolhouse2() adotx_m_woolhouse2() nax_m_woolhouse2() nadotx_m_woolhouse2() axn_m_woolhouse2() adotxn_m_woolhouse2() sxn_m_woolhouse2() sdotxn_m_woolhouse2() abarx_woolhouse2(): Woolhouse 2-term annuity approximations
ax_m_woolhouse3() adotx_m_woolhouse3() nax_m_woolhouse3() nadotx_m_woolhouse3() axn_m_woolhouse3() adotxn_m_woolhouse3() abarx_woolhouse3(): Woolhouse 3-term annuity approximations

Funding Plans for Contingent Contracts

Px() Pxn1() PnEx() Pxn() tPx() tPxn1() tPnEx() tPxn() PnAx() tPnAx() Pbarx() Pbarxn1() Pbarxn() PbarAbarx() PbarAbarxn1() PbarAbarxn() Px_m() Pxn1_m() Pxn_m() PnAx_m() EL0x() varL0x() EL0xn1() varL0xn1() EL0xn() varL0xn() EL0barAbarx() varL0barAbarx() Gx(): Chapter 9 premium, loss, and expense functions

Contingent Contract Reserves

tVx(): Whole life net level premium reserve
tVxn1(): Term insurance net level premium reserve
tVnEx(): Pure endowment net level premium reserve
tVxn(): Endowment insurance net level premium reserve
htVx(): h-pay whole life net level premium reserve
ELtx(): Mean present value of loss at duration t for whole life insurance
varLtx(): Variance of present value of loss at duration t for whole life insurance
tVbarx(): Whole life reserve with continuous premiums
tVbarAbarx(): Fully continuous whole life reserve
tVx_m(): Whole life reserve with m-thly premiums
GT_disc(): Total gain for a discrete insurance contract
GM_disc(): Mortality gain for a discrete insurance contract
GI_disc(): Interest gain for a discrete insurance contract
GT_cont(): Total gain for a continuous-style one-step recursion
GM_cont(): Mortality gain helper for continuous-style recursion
GI_cont(): Interest gain helper for continuous-style recursion
tVx_ret(): Whole life net level premium reserve by retrospective method
tVxn_ret(): Endowment insurance reserve by retrospective method
tVxn1_ret(): Term insurance reserve by retrospective method
tVnAx() htVnAx(): Deferred insurance reserve functions
PnAdotx(): Deferred annuity-due premium
tVnAdotx(): Deferred annuity-due reserve
Pnax(): Deferred annuity-immediate premium
tVnax(): Deferred annuity-immediate reserve
thiele_backward_step(): One backward Euler-style Thiele step
thiele_dVdt(): Reserve derivative from Thiele's equation
thiele_backward_path(): Backward Euler reserve path from maturity

Reserves as Financial Liabilities

alphaF(): Full preliminary term first-year modified premium
betaF(): Full preliminary term renewal modified premium
tVFx(): Full preliminary term reserve for whole life insurance
tsVx(): Fractional-duration whole life reserve
meanVx(): Mean reserve for whole life insurance
tsVxn(): Fractional-duration endowment reserve
tsVxn1(): Fractional-duration term reserve
tVGx(): Whole life gross premium reserve
tVEx(): Whole life expense reserve
GTg_disc(): Total gross gain for a discrete insurance contract
decompGg_disc(): Ordered gross gain decomposition

Multi-Life Models

tpxy(): Joint-life survival probability
tqxy(): Joint-life failure probability
tpxybar(): Last-survivor survival probability
tqxybar(): Last-survivor failure probability
tqxy1(): Probability that (x) fails before (y) within n years
tqyx1(): Probability that (y) fails before (x) within n years
tqxy2(): Probability that (x) fails after (y) within n years
tqyx2(): Probability that (y) fails after (x) within n years
nExy(): Joint-life pure endowment
nExybar(): Last-survivor pure endowment
adotxyn(): Joint-life temporary annuity-due
axyn(): Joint-life temporary annuity-immediate
adotxy(): Joint-life whole life annuity-due
axy(): Joint-life whole life annuity-immediate
Axyn1(): Joint-life term insurance
Axyn(): Joint-life endowment insurance
Axy(): Joint-life whole life insurance
adotxybarn(): Last-survivor temporary annuity-due
axybarn(): Last-survivor temporary annuity-immediate
adotxybar(): Last-survivor whole life annuity-due
axybar(): Last-survivor whole life annuity-immediate
Axybarn1(): Last-survivor term insurance
Axybarn(): Last-survivor endowment insurance
Axybar(): Last-survivor whole life insurance
ax_y(): Reversionary annuity to (y) after death of (x)
ay_x(): Reversionary annuity to (x) after death of (y)
abarx_y(): Continuous reversionary annuity to (y) after death of (x)
abary_x(): Continuous reversionary annuity to (x) after death of (y)
abarxy(): Continuous joint-life whole life annuity
abarxybar(): Continuous last-survivor whole life annuity
Abarxy(): Continuous joint-life whole life insurance
Abarxybar(): Continuous last-survivor whole life insurance
Abarxy1(): Continuous contingent insurance: benefit on death of (x) if before (y)
Abaryx1(): Continuous contingent insurance: benefit on death of (y) if before (x)
Abarxy2(): Continuous contingent insurance: benefit on death of (x) if after (y)
Abaryx2(): Continuous contingent insurance: benefit on death of (y) if after (x)

Multiple-Decrement Models

qxtau(): Total probability of decrement \(q_x^{(\tau)}\)
pxtau(): Survival probability \(p_x^{(\tau)}\)
dxj(): Cause-specific decrements \(d_x^{(j)}\)
dxtau(): Total decrements \(d_x^{(\tau)}\)
md_table(): Build a multiple-decrement table
npxtau_md(): \({}_n p_x^{(\tau)}\) from a multiple-decrement table
nqxj_md(): \({}_n q_x^{(j)}\) from a multiple-decrement table
nqxtau_md(): \({}_n q_x^{(\tau)}\) from a multiple-decrement table
tpxprimej_cf(): Single-decrement survival probability \({}_t p_x^{\prime(j)}\) under constant force
tqxprimej_cf(): Single-decrement failure probability \({}_t q_x^{\prime(j)}\) under constant force
tpx_tau_cf(): Total survival probability \({}_t p_x^{(\tau)}\) under constant forces
tqxj_cf(): Cause-specific probability \({}_t q_x^{(j)}\) under constant forces
qx_dep_cf(): Dependent probabilities \(q_x^{(j)}\) from independent probabilities \(q_x^{\prime(j)}\) under constant force
qxprime_mudd(): Independent probabilities \(q_x^{\prime(j)}\) from dependent probabilities \(q_x^{(j)}\) under MUDD
tqxprime_mudd(): Independent probabilities \({}_t q_x^{\prime(j)}\) under MUDD
qx_dep_sudd(): Dependent probabilities \(q_x^{(j)}\) from independent probabilities \(q_x^{\prime(j)}\) under SUDD
qxprime_sudd(): Independent probabilities \(q_x^{\prime(j)}\) from dependent probabilities \(q_x^{(j)}\) under SUDD

Multiple-Decrement Applications

Axj_md(): Discrete multiple-decrement insurance APV \(A_{x}^{(j)}\)
Abarxj_md(): Continuous multiple-decrement insurance APV \(\overline{A}_{x}^{(j)}\)
AS_path(): Projected asset share path \({}_{k}AS\)
AS_path_md(): General projected asset share path (multiple decrements)
tp00_tp01_euler(): Euler approximation for \({}_{t}p_{x}^{00}\) and \({}_{t}p_{x}^{01}\)
Pbar_trapz_ms(): Continuous premium approximation \(\overline{P}\) by trapezoidal rule
thiele_dVdt_01(): Reserve derivatives for the disability model with recovery
thiele_path_01(): Backward reserve path for the disability model with recovery
markov_nstep_prob(): n-step transition probability for a discrete-time Markov chain
gain_loss_md(): Gain or loss in a multiple-decrement model

Variable Interest Models

nEx_var() Axn1_var() Axn_var() axn_var(): Variable-interest actuarial present value functions
nEx_spot() Axn1_spot() Axn_spot() axn_spot(): Spot-rate actuarial present value functions
vt_var(): Discount factors under a variable annual interest scenario
pv_spot_cashflows(): Present value of cash flows using spot rates
z_from_coupon_semi(): Bootstrap semiannual nominal spot rates from coupon-bond yields
z_from_coupon_annual(): Bootstrap annual spot rates from annual coupon-bond yields
fnk_from_z(): Forward rate \(f_{n,k}\) from spot rates
forward_matrix_from_z(): Matrix of all determinable forward rates from spot rates
z_from_fn1(): Spot rates from forward one-year rates

Universal Life Insurance

coi_ul_typeB(): Cost of insurance for Type B universal life
AV_path_ul_typeB(): Account-value path for Type B universal life
AV_path_ul_typeA(): Account-value path for Type A universal life
iP_eiul(): Point-to-point index growth rates
iMA_eiul(): Monthly-average index growth rate
i_credit_eiul(): Credited rates from raw index growth rates
pxtau_ul(): One-year persistency rates for universal life
tpxtau_ul(): Cumulative persistency to the end of each policy year
GMF_rollforward_ul(): Guaranteed maturity fund roll-forward
rt_ul(): Ratio \(r_t = AV_t / GMF_t\) capped at 1
Vprefloor_crvm_ul(): Pre-floor CRVM reserve for universal life
ag38_prefunding_ratio(): AG 38 prefunding ratio
ag38_reserve_ul(): AG 38 reserve calculation

Profit Analysis

Pr_vector_disc(): Profit vector for a discrete profit-analysis model
Pi_signature(): Profit signature from a profit vector
NPV_profit(): Net present value of a profit signature
NPV_partial(): Partial net present values
discounted_payback_period(): Discounted payback period
IRR_profit(): Internal rate of return of a profit signature
APV_gross_premiums(): APV of gross premiums under a risk discount rate
profit_margin(): Profit margin
V_zeroized(): Zeroized reserves for a discrete death-only contract

Pension Benefits

salary_scale(): Salary scale under constant annual growth
AVz_dc(): Accumulated value of defined contribution plan contributions
Income_dc(): Retirement income from a defined contribution accumulation
replacement_ratio_dc(): Replacement ratio for a defined contribution plan
contribution_rate_target(): Target contribution rate for a defined contribution plan
PAB_fas(): Projected annual benefit under a final average salary DB plan
PAB_cae(): Projected annual benefit under a career average earnings DB plan
replacement_ratio_db(): Replacement ratio for a defined benefit plan
AB_fas(): Accrued benefit for a final average salary plan
AB_cae(): Accrued benefit for a career average earnings plan
APV_NR_db(): APV of normal retirement benefit for a DB plan
NC_EAN_db(): Entry Age Normal normal cost for a DB plan
NC_TUC_db(): Traditional Unit Credit normal cost for a DB plan
AAL_TUC_db(): Traditional Unit Credit accrued liability for a DB plan
NC_PUC_db(): Projected Unit Credit normal cost for a DB plan
AAL_PUC_db(): Projected Unit Credit accrued liability for a DB plan