In terms of the future curtate
lifetime K (x) at age x, the present value of benefits of 1 per year is an annuity for K(x) years:
Four special cases are, (1) If this component is positive, the trajectory is a curtate
cycloid; (2) If this component is negative, the trajectory is a prolate cycloid; (3) If this component is zero, the trajectory is a cycloid; and (4) If this component is equal to the electromagnetic drift velocity, the trajectory is a straight line; both the curvature and torsion of the path are zeros.
Their methodology (Difference in Curtate
Life Expectancy, or DCLE) was tested against the Fasano Associates database of over 50,000 unique lives and generated a difference between Actual and Expected of only 0.
Let us now illustrate this using the information about the insured most commonly used in life settlements: the medical underwriter has developed an estimate that the curtate
expectation of life for the individual whose policy is being settled is m years.