Reserve Valuation for Decreasing Life Insurance
Calculates the reserve for the decreasing life insurance up to the moment t.
V_AD.( px, x, h, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )
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 fractions 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).variation: A character string. "inter" if the variation it's inter-annual or "intra" if it's intra-annual.cap: A numeric type value. Amount insured for the first year/period.t: An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not).A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
V_AD.(251.489227521537,20,2,2,1,2,1,0.04,CSO80MANB,1,"none","none",100000,4) V_AD.(432.974179723949/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"UDD","intra",100000,48) V_AD.(258.794207318685/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"UDD","inter",100000,48) V_AD.(412.784641829906/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"constant","intra",100000,48) V_AD.(258.189935788232/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48)
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
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