Actuarial Risk Modeling and Life Contingencies
![[R logo]](../../../doc/html/Rlogo.svg)
![[Up]](../../../doc/html/left.jpg)
![[Top]](../../../doc/html/up.jpg)
Documentation for package ‘mqriskR’ version 0.1.0
Help Pages
A B C D E F G H I 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 for a DB plan |
| AAL_TUC_db | Traditional Unit Credit accrued liability for a DB plan |
| Abarx | Continuous whole life insurance APV |
| abarx | Annual annuity functions (Chapter 8) |
| Abarxj_md | Continuous multiple-decrement insurance APV \overline{A}_{x}^{(j)} |
| Abarxn | Continuous endowment insurance APV |
| abarxn | Annual annuity functions (Chapter 8) |
| 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 joint-life whole life insurance |
| abarxy | Continuous joint-life whole life annuity |
| 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 |
| abarxybar | Continuous last-survivor whole life annuity |
| abarxybar_ch12 | Continuous last-survivor whole life annuity |
| abarxy_ch12 | Continuous joint-life whole life annuity |
| 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 reversionary annuity to (y) after death of (x) |
| Abaryx1 | Continuous contingent insurance: benefit on death of (y) if before (x) |
| Abaryx2 | Continuous contingent insurance: benefit on death of (y) if after (x) |
| abary_x | Continuous reversionary annuity to (x) after death of (y) |
| AB_cae | Accrued benefit for a career average earnings plan |
| AB_fas | Accrued benefit for a final average salary plan |
| adotx | Annual annuity functions (Chapter 8) |
| adotxn | Annual annuity functions (Chapter 8) |
| adotxn_m | Temporary m-thly annuity-due |
| 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 whole life annuity-due |
| adotxybar | Last-survivor whole life annuity-due |
| adotxybarn | Last-survivor temporary annuity-due |
| adotxyn | Joint-life temporary annuity-due |
| adotx_m | Whole life m-thly annuity-due |
| 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 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_identity_abarx | Annuity-insurance relationships (Chapter 8) |
| annuity_identity_abarxn | Annuity-insurance relationships (Chapter 8) |
| annuity_identity_adotx | Annuity-insurance relationships (Chapter 8) |
| annuity_identity_adotxn | Annuity-insurance relationships (Chapter 8) |
| annuity_identity_ax | Annuity-insurance relationships (Chapter 8) |
| annuity_identity_axn | Annuity-insurance relationships (Chapter 8) |
| annuity_identity_nabarx | Annuity-insurance relationships (Chapter 8) |
| annuity_identity_nadotx | Annuity-insurance relationships (Chapter 8) |
| annuity_identity_nax | Annuity-insurance relationships (Chapter 8) |
| 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) |
| APV_gross_premiums | APV of gross premiums under a risk discount rate |
| APV_NR_db | APV of normal retirement benefit for a DB plan |
| AS_path | Projected asset share path {}_{k}AS |
| AS_path_md | General projected asset share path (multiple decrements) |
| AVz_dc | Accumulated value of defined contribution plan contributions |
| AV_path_ul_typeA | Account-value path for Type A universal life |
| AV_path_ul_typeB | Account-value path for Type B universal life |
| Ax | Whole life insurance APV |
| ax | Annual annuity functions (Chapter 8) |
| Axj_md | Discrete multiple-decrement insurance APV A_{x}^{(j)} |
| Axn | Endowment insurance APV |
| axn | Annual annuity functions (Chapter 8) |
| Axn1 | Term insurance APV |
| Axn1_m | m-thly term insurance APV |
| Axn1_m_udd | UDD approximation of m-thly term insurance |
| Axn1_spot | Spot-rate actuarial present value functions |
| Axn1_var | Variable-interest actuarial present value functions |
| axn_improved | Temporary annuity-immediate under mortality improvement |
| Axn_m | m-thly endowment insurance APV |
| axn_m | Temporary m-thly annuity-immediate |
| 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 | Spot-rate actuarial present value functions |
| axn_spot | Spot-rate actuarial present value functions |
| Axn_var | Variable-interest actuarial present value functions |
| axn_var | Variable-interest actuarial present value functions |
| Axy | Joint-life whole life insurance |
| axy | Joint-life whole life annuity-immediate |
| Axybar | Last-survivor whole life insurance |
| axybar | Last-survivor whole life annuity-immediate |
| Axybarn | Last-survivor endowment insurance |
| axybarn | Last-survivor temporary annuity-immediate |
| Axybarn1 | Last-survivor term insurance |
| axybarn_ch12 | Last-survivor temporary annuity-immediate |
| axybar_ch12 | Last-survivor whole life annuity-immediate |
| Axyn | Joint-life endowment insurance |
| axyn | Joint-life temporary annuity-immediate |
| Axyn1 | Joint-life term insurance |
| axyn_ch12 | Joint-life temporary annuity-immediate |
| axy_ch12 | Joint-life whole life annuity-immediate |
| ax_improved | Whole life annuity-immediate under mortality improvement |
| Ax_m | m-thly whole life insurance APV |
| ax_m | Whole life m-thly annuity-immediate |
| 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 to (y) after death of (x) |
| ay_x | Reversionary annuity to (x) after death of (y) |
-- B --
| betaF | Full preliminary term renewal modified premium |
-- C --
| 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 |
-- D --
| Dabarxn | Varying-payment annuity functions (Chapter 8) |
| DAbarxn1 | Piecewise-continuous decreasing n-year term insurance |
| Dadotxn | Varying-payment annuity functions (Chapter 8) |
| Daxn | Varying-payment annuity functions (Chapter 8) |
| DAxn1 | Decreasing n-year term insurance |
| DbarAbarxn1 | Fully continuous decreasing n-year term insurance |
| 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)} |
-- E --
| EL0barAbarx | Chapter 9 premium, loss, and expense functions |
| EL0x | Chapter 9 premium, loss, and expense functions |
| EL0xn | Chapter 9 premium, loss, and expense functions |
| EL0xn1 | Chapter 9 premium, loss, and expense functions |
| ELtx | Mean present value of loss at duration t for whole life insurance |
| 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 |
-- F --
| F0 | Distribution functions for age-at-failure T0 |
| f0 | Distribution functions for age-at-failure T0 |
| 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 |
-- G --
| gain_loss_md | Gain or loss in a multiple-decrement model |
| 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 |
| 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 | Chapter 9 premium, loss, and expense functions |
-- H --
| hazard0 | Hazard / force for age-at-failure T0 |
| htVnAx | Deferred insurance reserve functions |
| htVx | h-pay whole life net level premium reserve |
-- I --
| IAbarx | Piecewise-continuous increasing whole life insurance |
| Iabarx | Varying-payment annuity functions (Chapter 8) |
| Iabarxn | Varying-payment annuity functions (Chapter 8) |
| Iadotx | Varying-payment annuity functions (Chapter 8) |
| Iadotxn | Varying-payment annuity functions (Chapter 8) |
| IAx | Increasing whole life insurance |
| Iax | Varying-payment annuity functions (Chapter 8) |
| Iaxn | Varying-payment annuity functions (Chapter 8) |
| 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 of a profit signature |
| i_credit_eiul | Credited rates from raw index growth rates |
-- L --
| 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 | 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 |
-- N --
| nAbarx | Continuous deferred insurance APV |
| nabarx | Annual annuity functions (Chapter 8) |
| nAbarx_udd | UDD approximation of continuous deferred insurance |
| nabarx_udd | UDD annuity approximations |
| nadotx | Annual annuity functions (Chapter 8) |
| nadotx_m | Deferred whole life m-thly annuity-due |
| 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 (Chapter 8) |
| naxn_improved | Deferred temporary annuity-immediate under mortality improvement |
| nAx_m | m-thly deferred insurance APV |
| nax_m | Deferred whole life m-thly annuity-immediate |
| 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 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 |
| ndx | Compute deaths over an n-year interval from a life table |
| nEx | Pure endowment APV |
| nExy | Joint-life pure endowment |
| nExybar | Last-survivor pure endowment |
| nEx_spot | Spot-rate actuarial present value functions |
| nEx_var | Variable-interest actuarial present value functions |
| 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 | {}_n p_x^{(tau)} from a multiple-decrement table |
| npx_select | Select-life survival probability |
| nqx | Compute n-year death probability from a life table |
| nqxj_md | {}_n q_x^{(j)} from a multiple-decrement table |
| nqxtau_md | {}_n q_x^{(tau)} from a multiple-decrement table |
| nqx_select | Select-life death probability |
-- P --
| PAB_cae | Projected annual benefit under a career average earnings DB plan |
| PAB_fas | Projected annual benefit under a final average salary DB plan |
| PbarAbarx | Chapter 9 premium, loss, and expense functions |
| PbarAbarxn | Chapter 9 premium, loss, and expense functions |
| PbarAbarxn1 | Chapter 9 premium, loss, and expense functions |
| Pbarx | Chapter 9 premium, loss, and expense functions |
| Pbarxn | Chapter 9 premium, loss, and expense functions |
| Pbarxn1 | Chapter 9 premium, loss, and expense functions |
| 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 | Chapter 9 premium, loss, and expense functions |
| Pnax | Deferred annuity-immediate premium |
| PnAx_m | Chapter 9 premium, loss, and expense functions |
| PnEx | Chapter 9 premium, loss, and expense functions |
| premium_ch9 | Chapter 9 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 cash flows using spot rates |
| Px | Chapter 9 premium, loss, and expense functions |
| Pxn | Chapter 9 premium, loss, and expense functions |
| Pxn1 | Chapter 9 premium, loss, and expense functions |
| Pxn1_m | Chapter 9 premium, loss, and expense functions |
| Pxn_m | Chapter 9 premium, loss, and expense functions |
| pxtau | Survival probability p_x^{(tau)} |
| pxtau_ul | One-year persistency rates for universal life |
| Px_m | Chapter 9 premium, loss, and expense functions |
| px_proj | Project one-year survival probability under mortality improvement |
| px_to_lx | Construct life-table values from p_x values |
-- Q --
| 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)} |
| 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 |
-- R --
| 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 |
-- S --
| S0 | Survival function for age-at-failure T0 |
| S0_to_lx | Convert survival probabilities to life-table values |
| salary_scale | Salary scale under constant annual growth |
| sbarxn | Annual annuity functions (Chapter 8) |
| sdotxn | Annual annuity functions (Chapter 8) |
| sdotxn_m | Temporary m-thly annuity-due actuarial accumulated value |
| 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 |
| sxn | Annual annuity functions (Chapter 8) |
| sxn_m | Temporary m-thly annuity-immediate actuarial accumulated value |
| sxn_m_udd | UDD annuity approximations |
| sxn_m_woolhouse2 | Woolhouse 2-term annuity approximations |
-- T --
| 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} |
| tPnAx | Chapter 9 premium, loss, and expense functions |
| tPnEx | Chapter 9 premium, loss, and expense functions |
| tPx | Chapter 9 premium, loss, and expense functions |
| tpx | Conditional survival probability for Tx |
| tPxn | Chapter 9 premium, loss, and expense functions |
| tPxn1 | Chapter 9 premium, loss, and expense functions |
| 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 |
| 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 |
| tqx | Conditional failure probability for Tx |
| tqxj_cf | Cause-specific probability {}_t q_x^{(j)} under constant forces |
| tqxprimej_cf | Single-decrement failure probability {}_t q_x^{\prime(j)} under constant force |
| tqxprime_mudd | Independent probabilities {}_t q_x^{\prime(j)} under MUDD |
| 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 |
| tqx_tab | Fractional failure probability from a life table |
| 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 |
| tVbarAbarx | Fully continuous whole life reserve |
| tVbarx | Whole life reserve with continuous premiums |
| tVEx | Whole life expense reserve |
| tVFx | Full preliminary term reserve for whole life insurance |
| tVGx | Whole life gross premium reserve |
| tVnAdotx | Deferred annuity-due reserve |
| tVnAx | Deferred insurance reserve functions |
| tVnax | Deferred annuity-immediate reserve |
| 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 | Term insurance reserve by retrospective method |
| tVxn_ret | Endowment insurance reserve by retrospective method |
| tVx_m | Whole life reserve with m-thly premiums |
| tVx_ret | Whole life net level premium reserve by retrospective method |
-- U --
| udd_continuous_multiplier | UDD multiplier for continuous insurance approximations |
| udd_mthly_multiplier | UDD multiplier for m-thly insurance approximations |
-- V --
| varL0barAbarx | Chapter 9 premium, loss, and expense functions |
| varL0x | Chapter 9 premium, loss, and expense functions |
| varL0xn | Chapter 9 premium, loss, and expense functions |
| varL0xn1 | Chapter 9 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 for universal life |
| vt_var | Discount factors under a variable annual interest scenario |
| V_zeroized | Zeroized reserves for a discrete death-only contract |
-- Z --
| 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 |