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
F0() f0(): Distribution functions for age-at-failure
hazard0(): Hazard or force of mortality for age-at-failure
cumhaz0(): Cumulative hazard for age-at-failure
tpx(): Conditional survival probability
tqx(): Conditional failure probability
fx(): Conditional density
ex_complete(): Complete expectation of life
ex_curtate(): Curtate expectation of life

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
ax_m() adotx_m() axn_m() adotxn_m() nax_m() nadotx_m() sxn_m() sdotxn_m(): m-thly contingent annuity functions
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
Iax() Iaxn() Daxn() Iadotx() Iadotxn() Dadotxn() Iabarx() Iabarxn() Dabarxn(): Varying-payment annuity functions
qx_proj() px_proj() tpx_improved() axn_improved() naxn_improved() ax_improved(): Mortality improvement projection functions
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(): 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 for a continuous-style recursion
GI_cont(): Interest gain for a continuous-style recursion
tVx_ret(): Retrospective whole life reserve
tVxn_ret(): Retrospective endowment insurance reserve
tVxn1_ret(): Retrospective term insurance reserve
tVnAx() htVnAx(): Deferred insurance reserves
PnAdotx(): Net premium for a deferred annuity-due
tVnAdotx(): Reserve for a deferred annuity-due
Pnax(): Net premium for a deferred annuity-immediate
tVnax(): Reserve for a deferred annuity-immediate
thiele_backward_step(): One backward numerical step for Thiele's equation
thiele_dVdt(): Reserve derivative from Thiele's equation
thiele_backward_path(): Backward reserve path from a terminal value

Reserves as Financial Liabilities

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

Multi-Life Models

tpxy() tqxy() tpxybar() tqxybar(): Multi-life survival and failure probabilities
tqxy1() tqyx1() tqxy2() tqyx2(): Contingent multi-life probabilities
nExy() nExybar(): Multi-life pure endowments
adotxyn() axyn() adotxy() axy(): Joint-life annuities
Axyn1() Axyn() Axy(): Joint-life insurance functions
adotxybarn() axybarn() adotxybar() axybar(): Last-survivor annuity functions
Axybarn1() Axybarn() Axybar(): Last-survivor insurance functions
ax_y() ay_x(): Reversionary annuity functions
abarxy() abarxybar() abarx_y() abary_x(): Continuous multi-life annuities
Abarxy() Abarxybar() Abarxy1() Abaryx1() Abarxy2() Abaryx2(): Continuous multi-life insurance

Multiple-Decrement Models

qxtau(): Total one-year decrement probability
pxtau(): Total one-year survival probability
dxj(): Cause-specific numbers of decrements
dxtau(): Total number of decrements
md_table(): Construct a multiple-decrement table
npxtau_md(): Multiple-decrement survival probability from a table
nqxj_md(): Cause-specific multiple-decrement probability from a table
nqxtau_md(): Total multiple-decrement probability from a table
tpxprimej_cf(): Single-decrement survival under a constant force
tqxprimej_cf(): Single-decrement failure under a constant force
tpx_tau_cf(): Total survival under constant cause-specific forces
tqxj_cf(): Cause-specific decrement probability under constant forces
qx_dep_cf(): Multiple-decrement probabilities under constant forces
qxprime_mudd(): Associated single-decrement probabilities under MUDD
tqxprime_mudd(): Fractional-year associated single-decrement probabilities under MUDD
qx_dep_sudd(): Multiple-decrement probabilities under SUDD
qxprime_sudd(): Associated single-decrement probabilities under SUDD

Multiple-Decrement Applications

Axj_md(): Discrete multiple-decrement insurance present value
Abarxj_md(): Continuous multiple-decrement insurance present value
AS_path(): Projected asset-share path for two decrement causes
AS_path_md(): General projected asset-share path
tp00_tp01_euler(): Euler approximation of disability-state probabilities
Pbar_trapz_ms(): Continuous premium approximation in a disability model
thiele_dVdt_01(): Reserve derivatives for a disability model with recovery
thiele_path_01(): Backward reserve path for a disability model with recovery
markov_nstep_prob(): Multi-step transition probability
gain_loss_md(): Gain or loss in a two-cause multiple-decrement model

Variable Interest Models

nEx_var() Axn1_var() Axn_var() axn_var(): Actuarial present values under variable annual interest rates
nEx_spot() Axn1_spot() Axn_spot() axn_spot(): Actuarial present values under spot rates
vt_var(): Discount factors under variable annual interest rates
pv_spot_cashflows(): Present value of deterministic cash flows using spot rates
z_from_coupon_semi(): Bootstrap semiannual nominal spot rates
z_from_coupon_annual(): Bootstrap annual effective spot rates
fnk_from_z(): Forward rate implied by spot rates
forward_matrix_from_z(): Matrix of forward rates implied by spot rates
z_from_fn1(): Spot rates from one-year forward rates

Universal Life Insurance

coi_ul_typeB(): Cost of insurance for Type B universal life
AV_path_ul_typeB(): Type B universal life account-value path
AV_path_ul_typeA(): Type A universal life account-value path
iP_eiul(): Point-to-point index growth rates
iMA_eiul(): Monthly-average index growth rate
i_credit_eiul(): Credited rates from index growth rates
pxtau_ul() tpxtau_ul(): Universal life persistency probabilities
GMF_rollforward_ul(): Guaranteed maturity fund roll-forward
rt_ul(): Account-value to guaranteed-fund ratio
Vprefloor_crvm_ul(): Pre-floor CRVM reserve
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
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
APV_gross_premiums(): Actuarial present value of gross premiums
profit_margin(): Profit margin
V_zeroized(): Zeroized reserves for a discrete death-benefit 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 plan
PAB_cae(): Projected annual benefit under a career-average-earnings plan
replacement_ratio_db(): Replacement ratio for a defined benefit plan
AB_fas(): Accrued benefit under a final-average-salary plan
AB_cae(): Accrued benefit under a career-average-earnings plan
APV_NR_db(): Actuarial present value of a normal retirement benefit
NC_EAN_db(): Entry Age Normal normal cost
NC_TUC_db(): Traditional Unit Credit normal cost
AAL_TUC_db(): Traditional Unit Credit accrued liability
NC_PUC_db(): Projected Unit Credit normal cost
AAL_PUC_db(): Projected Unit Credit accrued liability