Actuarial Science 2427A/B Lecture Notes - Lecture 18: Life Annuity, Contin, Rary
14 Jun 2018
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AS2427 Ch.5 Lecture Notes March 29, 2018
1
5.1 Summary
5.2 Intro
5.3 Term Certain Annuity Review
5.4 Annual Life Annuities
5.5 Annuities payable continuously
5.6 Annuities payable m-times per year
5.7 Comparison of Annuities by payment frequency
5.8 Deferred annuities **
5.9 Guaranteed annuities **
5.10 Increasing Annuities(Geometric, Arithmetic)
5.11 Evaluating Annuity functions-recursions(**) and approximations
5.12 Numerical Illustrations
5.13 Functions for select lives **
Note:
some topics (e.g. **) will be covered in different order than text
Any additions/updates to these notes will be announced in class
find more resources at oneclass.com
find more resources at oneclass.com
AS2427 Ch.5 Lecture Notes March 29, 2018
2
•
What is a Life Annuity?
“
a series of payments made continuously or at equal intervals (such as
monthly), while a given life survives”
payments are contingent on survival
• many different life annuity types and applications, including
- retail product
- Life Insurance Premium & Benefit Determinations(Ch. 6– Life Cons II)
Most policy premiums payable annually or monthly
- pension plans-benefit at retirement (and funding of benefits)
covered later in text (and in upper year courses)
- disability insurance
- settlements
•
will review various types of life annuities, their IAN, how to value
them, relationship to insurances, and relationship between
different annuity types and approximations used
o material builds upon annuity certain concepts covered in AS2553
find more resources at oneclass.com
find more resources at oneclass.com
AS2427 Ch.5 Lecture Notes March 29, 2018
3
•
General Types of Life Annuities
1) ; payments for as long as person is living
2) Temporary Life Annuities; payments for at most n years
(as long as living)
3) Deferred Life Annuities; whole life with 1
st
payment deferred m years
4) Deferred Temporary Life Annuities-temporary life annuity with at
most n payments, where 1
st
payment deferred m years
• can look at categorizing each of the above types further;
Payment frequency; annual(5.4) “mthly” (5.6) or continuous (5.5)
if discrete, are payments at beginning(due) or end (immediate) of
period
varying payments (step-rate, geometric, arithmetic or other)
• majority of life annuities are payable more frequently than annually so
often need approximations for fractional periods
• as with life insurance, annuity values can be generated recursively and
select rates can be used
• life annuities are also often sold with a guarantee period and this can
be readily handled for any type of life annuity
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
As2427 ch. 5 lecture notes march 29, 2018 (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:8)(cid:11)(cid:12)(cid:13)(cid:6)(cid:8)(cid:14)(cid:15)(cid:15)(cid:16)(cid:12)(cid:5)(cid:12)(cid:6)(cid:17)(cid:8) Note: some topics (e. g. **) will be covered in different order than text. Any additions/updates to these notes will be announced in class. 6 life cons ii) (cid:2) most policy premiums payable annually or monthly. Pension plans-benefit at retirement (and funding of benefits) (cid:2) covered later in text (and in upper year courses) Settlements: will review various types of life annuities, their ian, how to value them, relationship to insurances, and relationship between different annuity types and approximations used, material builds upon annuity certain concepts covered in as2553. As2427 ch. 5 lecture notes march 29, 2018 (cid:9)(cid:18)(cid:31)(cid:8)(cid:14)(cid:15)(cid:15)(cid:16)(cid:12)(cid:5)(cid:28)(cid:8)(cid:1)(cid:6)(cid:7)(cid:5)(cid:3)(cid:12)(cid:15)(cid:8) (cid:24)(cid:7)(cid:27)(cid:16)(cid:30)(cid:3)(cid:17)(cid:8)(cid:7)(cid:6)(cid:13)(cid:6)(cid:7)(cid:6)(cid:15)! (cid:6)(cid:25)(cid:8) = 1+ v +v2 +v3 +v4 + +v n-1 = (1- vn)/d (where d=i/(1+i)) a(cid:1)(cid:1) |n a = v +v2 +v3 +v4 + +v n = (1- vn)/i = ( 1 +vn ) n a = (cid:1)(cid:1)(cid:1)(cid:1) )m( a = 1/m (v1/m + v2/m + v3/m + .
