V_a function

Reserve Valuation for Life Annuities

Calculates the reserve for the life Annuity up to the moment 't'.

V_a(
  px,
  x,
  h,
  n,
  k = 1,
  cantprem = 1,
  premperyear = 1,
  i = 0.04,
  data,
  prop = 1,
  assumption = "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.
• 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).
• cap: A numeric type value. The annualized value of the payment.
• t: An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not).

Returns

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

Examples

V_a(147.814202915034,20,5,10,1,5,1,0.04,CSO80MANB,1,"none",100,15)
V_a(148.324902023591/12,20,5,10,4,60,12,0.04,CSO80MANB,1,"constant",100,178)
V_a(223633.861110949,25,0,25,12,10,1,0.04,CSO80MANB,1,"UDD",120000,300)

References

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