Exposed to risk census approximations policy year

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Unformatted text preview: t the policy anniversary preceding death” at the start of the rate interval (policy year) ages range from x exact to x + 1 exact assume a uniform distribution of birthdays with respect to policy anniversaries 1 q estimates qx + 2 and µ estimates µx +1 14/35 Actuarial Statistics – Module 7: Exposed to risk Census approximations “Policy Year” rate interval Distribution of policy anniversaries over the year Assumptions about distribution of policy anniversaries need to be treated with care. For example: some policies tend to be taken out in large numbers just before the end of the tax year there might a tendency to take out policies just before dates upon which premium would rise under group schemes, where insurance cover for employees is provided by the employer, the policy anniversaries might all be the same (in which case we have both a policy year rate interval and a calendar year rate interval) 15/35 Actuarial Statistics – Module 7: Exposed to risk Examples Definition of x 1 Introduction Central vs Initial Exposed to Risk Complete data Incomplete data 2 Census approximations Introduction “Calendar Year” rate interval “Policy Year” rate interval 3 Examples Definition of x Trapezium approximation Estimation Principle of correspondence Calendar year rate intervals Policy year rate intervals 16/35 Actuarial Statistics – Module 7: Exposed to risk Examples Definition of x Example: Age last birthday A mortality investigation covers the period 1 Jan 2001 to 31 Dec 2003. In this investigation, the age label used is “age last birthday”. Give the range of dates for which the lives in the following table c contribute to Ex for all relevant x ’s in the investigation period. Assume that the day of entry counts in the exposed to risk but the day of exit does not. Date of birth Date of Entry Date of exit Reason for exit A 25.04.69 07.08.99 30.10.02 Death B 01.07.69 12.09.02 - 16/35 Actuarial Statistics – Module 7: Exposed to risk Examples Definition of x A: The life joins the investigation at age 31 last birthday. It’s contribution to c E31 : 01.01.01 to 24.04.01 c E32 : 25.04.01 to 24.04.02 c E33 : 25.04.02 to 29.10.02 B: The second life joins the investigation at age 33 last birthday. It’s contribution to c E33 12.09.02 to 30.06.03 c 01.07.03 to 31.12.03 E34 17/35 Actuarial Statistics – Module 7: Exposed to risk Examples Definition of x Example: Age next birthday Now suppose that for the same mortality investigation covers the period 1 Jan 2001 to 31 Dec 2003, the age label used is “age next birthday”. c Give the range of dates for which life A contribute to Ex at each age where it makes a contribution. Date of birth Date of Entry Date of exit Reason for exit 25.04.69 07.08.99 30.10.02 Death The life joins the investigation at age 32 next birthday. It’s contribution to c E32 : 01.01.01 to 24.04.01 c E33 : 25.04.01 to 24.04.02 c E34 : 25.04.02 to 29.10.02 18/35 Actuarial Statistics – Module 7: Exposed to risk Examples Trapezium approximation 1 Introduction Central vs Initial Exposed to Risk Complete data Incomplete data 2 Census approximations Introduction “Calendar Year” rate interval “Policy Year” rate interval 3...
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This document was uploaded on 04/03/2014.

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