V_av {DetLifeInsurance}

Reserve Valuation for Varying Life Annuities: Arithmetic Progression

Description

Calculates the reserve for the Varying Life Annuity up to the moment t.

Usage

V_av(
  px,
  x,
  h,
  n,
  k = 1,
  r,
  cantprem = 1,
  premperyear = 1,
  i = 0.04,
  data,
  prop = 1,
  assumption = "none",
  variation = "none",
  cap,
  t
)

Arguments

px

A numeric value. The value of the premium paid in each period.

x

An integer. The age of the insuree.

h

An integer. The deferral period.

n

An integer. Number of years of coverage.

k

An integer. Number of payments per year.

r

The variation rate. A numeric type value.

cantprem

An integer. The total number of premiums.

premperyear

An integer. The number of premiums to be paid per year.

i

The interest rate. A numeric type value.

data

A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death.

prop

A numeric value. It represents the proportion of the mortality table used (between 0 and 1).

assumption

A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage).

variation

A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual.

cap

A numeric type value. The annualized value of the first payment.

t

An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not).

Value

A data frame with Premium, Risk, 1/E and reserve values up to the moment t.

References

Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.

Examples

V_av(9435943.49607651,20,2,2,1,0.05,2,1,0.04,CSO80MANB,1,"none","none",10000000,4)
V_av(9516712.17583443/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","inter",10000000,48)
V_av(9517.04683383614/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","inter",10000,48)
V_av(997.404109454868/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","intra",1000,48)
V_av(997436.738989113/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","intra",1000000,48)
V_av(28.4421691213902,40,3,7,2,0.7,1,1,0.04,CSO80MANB,1,"UDD","intra",1,120)