Actuarial Risk Modeling and Life Contingencies
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Documentation for package ‘mqriskR’ version 0.1.1
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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 |