Single-life fractional survival and complete life expectancy retain small annual survival derived from survivor counts. CF and Balducci avoid cancellation through mortality complements and use logarithmic ratios when annual survival underflows; integer horizons and table truncation conventions are preserved.
Monte Carlo summaries retain representable standard deviations and standard
errors when variance loses range. Empirical TVaR integrates ordered tail
masses without overflowing excess-loss differences, preserving fractional
atoms, signed values and endpoint conventions. Empty probability selectors
omit their columns and empty grouped summaries retain their schema.
The independence assumption behind se_mean and antithetic limits are
documented explicitly; no pairing is inferred from a method label.
Monte Carlo premium, loss and reserve consumers accept overflowing annualized annuity-basis metadata only when they match a finite per-payment basis and frequency. Inconsistent metadata and inference from an infinite annualized value alone remain errors, preserving valid chained monetary calculations.
mc_reserve moment-of-death pure endowments require
survival strictly beyond maturity. Internally estimated premiums retain
their scale interpretation regardless of the input premium-unit selector;
supplied premiums retain their declared units.
Monte Carlo reserves value future monetary flows with the original log interest rate. Known uncovered benefits remain zero, missing issue annuities are excluded as complete estimation pairs, and actual premium income retains range independently of its displayed annuity basis. Coincident flows can cancel despite separate present-value overflow. Existing in-force and before/after-payment conventions are clarified.
Monte Carlo premiums and losses retain representable monetary amounts when an intermediate annuity-scale coefficient underflows or overflows. Scaled means preserve positive subnormal premium exposure, and large valid payment frequencies retain numeric storage. Existing paired-NA, grouping and premium unit conventions are retained; displayed unrepresentable coefficients and amounts retain their double-precision limits.
Moment-of-death pure endowments in mc_insurance require
survival strictly beyond maturity. A death exactly at maturity belongs
to the term component, making term plus pure endowment equal endowment
on each trajectory. The annual curtate convention is retained.
Pathwise Monte Carlo annuities and insurance retain the original log interest rate and representable monetary cash flows at extreme rates. Zero amounts, payments at time zero, unknown lifetimes and existing payment calendars retain their meanings. Large conversion frequencies preserve numeric storage; invalid payment frequencies fail before integer coercion.
Single-life simulation wrappers retain finite constant-force lifetimes when annual survivor ratios underflow. Valuation uses the original interest convention and stable monetary annuity sums, including small period rates. Invalid ranges and incompatible survivor counts fail before coercion or sampling. Finite-horizon censoring and existing random-stream conventions are retained and clarified.
Multiple-life simulated statuses require the exact lifetime relation K <= T < K+1 before aggregation; tolerance still checks integer K. Complete lifetimes are rejected rather than repaired. Large curtate status values retain numeric storage, and identifier/output-name collisions give an explicit error. Existing valid min/max results and schemas are retained.
Lifetime simulation retains positive annual survival under CML and Balducci even below the checking tolerance. Simulation from survivor counts uses direct decrements and positive exposure independently of the radix. Invalid tolerances and out-of-range ages fail before integer coercion; valid terminal death ages retain values beyond integer storage. Seeded calls preserve their existing random-stream and restoration conventions.
Two-life fractional survival retains tiny observed annual survival in log form. Complete two-life expectancy uses analytic annual UDD, constant-force and Balducci integrals, avoiding quadrature loss near steep mortality. Existing conditioning, zero-duration and open-table truncation are retained.
Two-life pure-endowment premiums and reserves use direct discounted status survival, retaining small benefits lost by subtracting insurance APVs. Joint reserves now use backward conditional recursion; last-survivor reserves retain their three-state model. Both use direct annual decrements and original log interest. Immediate premiums include those due exactly at the reserve date, including a scheduled last installment at maturity.
Two-life annuities retain tiny designated-reversion probabilities, original log interest and representable signed monetary payments on fractional grids. Annual-table and payment-grid consistency are checked explicitly. Second-order Woolhouse corrections require supported positive borders and following years; negative approximations warn without clipping. State meanings and open-table truncation limits are documented without changing the signature.
Two-life insurance sums disjoint annual first/second-death transition masses from issue, retaining tiny mortality and representable monetary values with extreme interest. State conditioning and existing audit columns are retained. Whole insurance without observed status extinction is rejected; a zero-term endowment pays at its deferred maturity.
Two-life survival and expectancy reject incompatible annual ages, increasing or invalid survivor counts and contradictory mortality probabilities. Invalid controls and out-of-range age coercions fail explicitly; existing initial-state, zero-duration and table-horizon conventions are preserved.
Two-life survival and expectancy normalize inherited CML attributes to
constant force, including equivalent CF/CML attributes on two tables.
annuity_multi() adds trailing frac, values actual payments
of 1/k under UDD, CF/CML or Balducci with woolhouse = "none", and includes
both deferred and terminal endpoints in temporary Woolhouse corrections.
The historical joint-and-survivor meaning of reversionary is clarified.
Variable subperiod death benefits use direct mortality masses and original log interest, retaining small decrements and representable extreme APVs. Coverage-relative functional benefit times and full payment amounts are documented. Invalid tables, horizons and payment grids fail explicitly.
Cause-specific annual insurance validates competing-exit probabilities and
consecutive ages, retains cumulative log survival and original interest,
and preserves its vectorized output and A_xj alias. Available-table whole
insurance is explicitly described as truncated when the table is open.
Life-contract specifications preserve large integer-valued inputs without coercing them to missing values and validate the financial domain of stored rates. Premium schedules reject overflowing or empty rounded payment grids; standard positive insurance terms cannot round to zero. Component schemas, ordinary integer types and original rate specifications are retained.
Net premiums use the actual term inferred from a variable benefit schedule, reject premiums beyond that coverage and accept aligned fractional variable terms. Invalid controls and integer coercion failures are checked explicitly.
Gross premiums validate monetary consistency independently of currency units, retain acquisition shares and small expense loadings, and factor the equivalence residual to avoid overflowing intermediate APV subtraction.
Single-life recursive reserves use the equivalent backward identity with a supported prospective boundary condition, preserving original rate growth, rare death/survival probabilities and nonzero whole-life terminal values. Unrequested extinct states are not traversed. Public signatures and output schemas remain unchanged.
annuity_x() and insurance_x() now value parallel single-life scenarios
on a shared mortality table, recycling only length-one arguments. Numeric
vectors work in mutate(); tidy output has one row per scenario. Missing or
incompatible scenario inputs fail explicitly. Existing formals are retained.
Exact single-life valuations retain original log interest and survival ratios, value deferred payments from issue, and handle extinct tails. Annual death probabilities use survivor decrements before division. Explicit interest overrides on insurance contracts are respected. Woolhouse reports negative approximations and rejects undefined positive-survival boundary forces.
Zero-term endowments pay on survival at deferred maturity.
Empty annuities retain zero APV, with a pure endowment factor
of one and the ordinary annuity_value_at_start diagnostic column.
Life cash-flow APVs retain original log interest rates and combine monetary, survival and discount factors before rounding the product. Rare last-survivor probabilities avoid subtractive cancellation. Missing numeric times remain missing rows; mortality queries are bounded by table size and preserve known extinction. Invalid mortality values, duplicate ages and infinite dates are rejected explicitly. The existing nonmissing APV subtotal is now documented; signatures, output columns and row order remain unchanged.
plot_contingent_cash_flow() plots payment-level contractual amounts,
unconditional event probabilities, expected cash flows and APV contributions.
It reuses apv_life_flow() outputs and accepts explicit discrete death-event
tables. Reversionary benefit weights are labeled separately from probabilities;
apv_life_flow() now attaches additive contingency metadata for this purpose.t_Ex() returns discounted survival without an upper cap of
one, allowing actuarial values above one under negative interest rates.
Pure endowments and commutation values retain original log discount rates.
Survival/death probabilities preserve small fractional decrement losses; complete expectancy integrals retain small horizons and treat extinct cohorts and unknown survivor counts without spurious NaN/index errors.
Kaplan-Meier ax measures time lived by interval decedents
in years. Empirical exposures are stable across radix scales and use the
CF/Balducci zero-survival limits; positive deaths at zero exposure yield Inf.
Standard errors and confidence limits retain very small survival estimates.
Multiple-decrement tables reject cause names that overwrite totals or other causes; fractional cause probabilities retain rare losses. Annual consumers validate annual age grids, and KM plots sort and validate step/band data.
Open life tables built only from lx now leave
terminal deaths/probabilities/central rates missing instead of implying certain
death. Supplied terminal probabilities and closed-table conventions remain.
Annual life tables reject contradictory qx/px, forbidden NaN values,
invalid controls/radices and unsupported integer ages. Input lengths are
checked before truncation; accepted near-integer ages are rounded consistently.
Mortality laws avoid intermediate power overflow in Gompertz/Makeham and Logistic forces. Weibull annual increments retain tiny positive hazards; Heligman-Pollard handles a unit childhood base with very large exponents.
Cash-flow diagrams retain finite graphical coordinates at extreme monetary
magnitudes, use scientific labels for tiny nonzero/very large amounts, reject
infinite dates explicitly and avoid unnecessary integer coercion of m.
Overlapping labels may be omitted while all arrows and payment times remain;
existing argument names, raw cash-flow columns and financial valuation remain.
Immunization retains original log liability rates and forms relative moments and scaled constraints before monetary products overflow. The existing minimum norm over asset units, SVD rank checks and sensitivity conventions are preserved; resulting portfolio measures must be finite.
Immunization gap plots combine signed weighted cash flows with log discounts, preserving finite surplus values and zero-weight assets when individual valuations lose range. The grid respects representable annual effective rates above -1; invalid grids and nonfinite gaps are rejected explicitly.
Cash-flow duration and convexity form relative contributions directly, avoiding overflowing monetary numerators and recovering representable discounted products. Signed near-cancellation checks remain unchanged.
Bond duration and convexity retain original log yields and normalized present-value moments. Calendar tolerances no longer reject small positive prices solely because of currency units; unsupported indices and truly nonrepresentable risk measures fail explicitly.
Portfolio duration and convexity avoid monetary products that overflow or underflow before taking a finite weighted average. Yield-coordinate and time-unit requirements for aggregation are now explicit in documentation.
With .na = "propagate", portfolio positions
with missing identifiers now produce a final row with an NA identifier and
missing sensitivity, value and position count, instead of silently vanishing.
Missing-value drop and error policies are preserved.
Spot discount and forward calculations retain original log growth rates, avoiding overflowed power ratios and preserving small rates and flat curves across intervals with large common origins. Linear interpolation remains on annual effective spot rates.
Par coupon rates separate monetary scale from discount sums and preserve small positive or negative coupons instead of rounding them to zero.
Missing spot curves keep their plot list positions; forward intervals with missing start times now follow the requested missing-value policy.
Bond book values retain original log yields when valuing remaining payments. Callable scenarios pass the original yield specification to pricing rather than an effective equivalent that may have rounded to -1 or overflowed.
Callable dates must identify distinct coupon periods strictly inside maturity after alignment; nonrepresentable period counts are rejected before integer conversion in book-value and callable schedules.
Callable is_worst_case now marks exactly the
computed minimum price and all exact computed ties. Calendar tolerance no
longer determines monetary near ties. Arguments and columns are unchanged.
Bond prices retain original log yields and recover representable discounted amounts when intermediate powers overflow or underflow. Coupon schedules and accrued interest also recover finite coupons from overflowing products.
Bond yields use a stable log price equation, avoiding bracket failures on ordinary long bonds and dependence on currency scale. Automatic brackets cover representable yields above -1; exhausted iterations now cause an error. Nonfinite tolerances, intervals and unsupported integer indices are rejected. Public arguments and result columns are preserved.
General amortization now identifies negative amortization under advance payments when accrued interest exceeds regular and extra payments combined.
Named extra-payment periods are checked before integer conversion, preventing fractional names from silently assigning prepayments to the wrong period.
Loan schedules require finite balance tolerances and reject nonrepresentable calculated payments or monetary ledgers explicitly. General level payments use a log discount sum to preserve finite payments when discounts overflow.
Arithmetic annuities retain original log rates and recover representable monetary products when standalone factors lose range, preserving signed and known zero payments.
Geometric annuities use stable log sums instead of subtracting nearly equal rates or accumulation levels. Small interest-growth spreads are retained before period conversion, and convergent perpetuities no longer face an arbitrary rate-gap cutoff. Missing finite terms propagate missing values.
Level annuities retain original log interest rates, small-rate effects over long terms and representable monetary values when standalone factors lose range. Strictly positive perpetuity rates no longer face an arbitrary cutoff.
Loan payments and sinking-fund deposits no longer use monetary balance tolerances to classify rates as zero. Period rates and variable-rate discount factors use original log growth. Public signatures and columns are preserved.
s_angle documentation now identifies the existing horizon as the end of the term, one payment interval after the final due payment.
solve_value() now has a trailing argument residual_tol = tol,
separating result-unit residual accuracy from unknown-coordinate accuracy.
Audit convergence uses this explicit threshold without a hidden floor.
Exhausting uniroot iterations is now an error. Existing positional arguments
and output columns are preserved; an audit flag can become more stringent.
Present/future cash-flow totals and inferred plot present values recover cancellation of overflowing terms with exactly equal finite log factors. Representable ordinary sums retain their existing evaluation; unequal-factor extreme cancellation remains outside this recovery rule.
Basic cash-flow valuations recover representable signed capital-factor products even when a separate factor overflows, underflows or is subnormal. Known zero payments stay zero without converting missing inputs to zero.
Newton solving now requires a small correction as well as a small residual; tiny residual units or a boundary-clipped step no longer imply convergence. Nonzero derivatives are no longer discarded by an absolute scale threshold.
Cash-flow plot present values now use the corrected financial basis. Unrepresentable aggregate amounts and inferred present values are rejected; tabular pipes, negative numeric timelines and editable ggplots are preserved.
IRR searches no longer classify small monetary NPVs as grid roots. Positive rescaling preserves roots across monetary units, sign checks avoid residual products, and reported NPVs retain the original currency. Scaling that would erase a nonzero cash flow is rejected explicitly.
solve_value interval scans now refine sign-changing brackets rather than treating all residuals below an absolute tolerance as distinct grid roots.
Interval factors, equivalent-rate tables and basic cash-flow valuations retain the original log accumulation rate when an annual effective equivalent rounds to -1 or overflows. Interval discounts no longer require a representable reciprocal accumulation. Future cash-flow ratios avoid overflow of their separate accumulation levels. Public schemas are retained; extreme annual-equivalent audit fields may still display -1 or Inf.
Rate conversions and accumulation/spot discount factors retain precision near zero using log1p and expm1. Small positive or negative rates no longer collapse to zero before conversion or lose their effect over long terms. Missing rate conventions now propagate missing equivalents as documented.
Deferred two-life insurance now retains survival conditioning from issue. Last-survivor continuation includes paths with only one survivor at the end of deferment, instead of restarting both lives at advanced ages. Its annuity and maturity-survival audit values use the same conditioning.
Fractional deferred Monte Carlo annuities now anchor their payment grid at the deferment rather than issue time. Non-grid-aligned deferments no longer omit eligible payments; the shared reserve calendar is corrected too.
Negative-binomial and geometric frequency thinning now avoids intermediate
overflow for tiny original prob. Conversions that would round a positive
payment frequency to zero now fail explicitly and retain the per-loss
model as the available representation.
Internal development instructions and audit records are excluded from source-package archives.
Life-contingent Monte Carlo insurance, annuity and reserve calculations now reject noninteger or infinite curtate lifetimes, infinite complete lifetimes, and observed pairs inconsistent with K <= T < K + 1. Missing values retain their existing meaning. Certain annuities remain independent of lifetime values. A shared internal validator prevents chained valuations from accepting contradictory versions of the same life.
Monte Carlo life annuities now preserve missing lifetime information as missing present values and payment counts, instead of zero payments. Certain annuities remain independent of lifetime data.
Fractional Monte Carlo annuity schedules now compare payment grid dates directly with the complete lifetime. A fixed epsilon no longer removes payments just before death or introduces payments just after death. Existing exact-death endpoint conventions are preserved.
Guaranteed fractional annuities retain their guaranteed payments even when death occurs at time zero. The shared payment schedule also serves Monte Carlo reserve and fractional annuity simulation calculations.
Last-survivor recursive reserves now use backward recursion across the both-alive and each single-survivor state. The previous scalar recursion mixed these conditioning states and disagreed with prospective reserves. Documentation explicitly conditions reserve_xy() on both lives being alive at valuation. Joint-life recursion and public output columns are preserved.
Constant-force fractional lifetime simulation now evaluates log(1-q) using log1p(-q). Tiny positive mortality probabilities no longer round the denominator to zero and collapse conditional death times to the year start.
Discrete VaR now compares the requested level directly with cumulative probabilities, without shifting it by an absolute epsilon. Levels just above an atom or the represented aggregate mass no longer select the previous atom or slip into an uncomputed tail.
VaR from FFT aggregates now checks whether omitted claim-count probability
could change the selected quantile, using the minimum possible loss of
omitted counts. Ambiguous quantiles are rejected with advice to reduce
tol. Documentation distinguishes unrepresented mass from an upper loss
tail: omitted large counts can still produce small aggregate losses.
Aggregate distributions now infer decimal lattices relative to the severity
magnitude and merge support points using relative monetary tolerances.
Small monetary units no longer collapse distinct losses into zero, and
convolution/FFT max_loss cutoffs respect the same scale. Strictly positive
masses below 1e-18 are retained rather than silently discarded.
Stop-loss premiums for covered exponential per-loss severities now use
closed forms for ordinary and franchise deductibles, inflation, coinsurance,
and finite or infinite limits. Very large limits no longer produce spurious
zero premiums through quadrature. Their reported method changes from
numerical_survival to closed_form; TVaR uses the corrected premiums too.
Immunization functions now use relative checks for liability present values and two-asset duration degeneracy, avoiding rejection of valid portfolios solely because of monetary units or small asset prices. Non-finite liability valuations and sensitivities are rejected explicitly.
Immunization systems with more assets than moment constraints now use row-scaled singular value decomposition for the minimum-norm asset units, instead of normal equations that could falsely classify distinct sensitivities as singular.
Clarified that immunize_duration_convexity() requires convexity with
respect to the annual effective yield. The coupon-frequency-scaled
bond_convexity() output generally uses a different yield variable;
documentation now gives the chain-rule conversion. Bond output meanings
are preserved. Examples now use convexities on the liability yield basis.
Corrected complete e_xy(..., cohort = "last") calculations to preserve
conditioning on both lives being alive at the initial ages. Annual
integration now uses survival from those original ages, including paths
with only one survivor, instead of restarting both lives each year.
Annual integrals use analytic UDD, constant-force, or Balducci formulas
for both cohorts, replacing numerical quadrature.
Missing initial ages and zero initial survivors return NA consistently.
t_px() now obtains integer survival directly from lx, including at
the last recorded age, without requiring a next-year probability.
An extinct attained cohort has zero survival even when its fractional
probability is undefined. This also prevents spurious NA in e_xy().
Corrected mortality_law_table("HeligmanPollard", ...) to the classical
eight-parameter odds model. H is now required; C is the childhood
exponent, D/E/F_hp describe the accident hump, and G/H describe
old-age mortality. Previous seven-parameter calls must be respecified;
adding H to the old values is insufficient. The existing F alias
denotes the same parameter as F_hp. Log-space evaluation avoids
undefined probabilities when odds overflow.
Beta-law conditional probabilities now use log upper-tail survival,
avoiding premature qx = 1 when survival is small.
Mortality-law tables now compute mx = dx / Lx and ex = Tx / lx
without artificial denominator floors. Zero-exposure positive deaths
give Inf; undefined 0/0 ratios for extinct cohorts give NaN.
mortality_law_table() now derives annual death probabilities from the
integrated continuous force of mortality, independently of frac.
This changes Gompertz, Makeham, Weibull and Logistic results and the former
UDD/Balducci conversions. mu_x remains the force at integer age;
a_x still controls the exposure approximation. Direct qx laws and
forced terminal closure retain their existing behavior.
Corrected lifetable() conversions between mx and qx for ax != 0.5,
using the mean fraction of the year lived by those who die. This correction
can change previous actuarial results; results for ax = 0.5 are preserved.
Fixed the construction of the cumulative distribution function used by
simulate_lifetime() to prevent platform-dependent numerical failures
when floating-point accumulation produces values slightly greater than one.
Added a regression test for the multiple-life simulation workflow using
simulate_lifetimes(), mc_multilife_status(), and mc_annuity().
This release addresses the errors reported by CRAN on macOS ARM64.
mc_annuity() examples.simulate_lifetimes() now constructs lifetime simulations defensively when mortality inputs contain invalid terminal values.mc_multilife_status() now uses defaults compatible with simulate_lifetimes(): sim_id, life_id, Kx, and Tx.