Actuarial Science 2427A/B Lecture Notes - Lecture 15: Ecall, Random Variable, Fop
14 Jun 2018
School
Department
Professor
AS2427 Chapter4 Lecture Notes – February 2018
1
4.1 Summary
4.2 Introduction
4.3 Assumptions
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AS2427 Chapter4 Lecture Notes – February 2018
2
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•
Chapter introduces international actuarial notations & formulas
for expected present value(EPV) for different life Insurances
o Second moments and variance are also covered
•
For each insurance type, will look at timing of when DB is paid
(i)
Payable at moment of death (continuous)
(ii)
Payable at end of year of death (discrete)
(iii)
Payable at end of mth period of death (also discrete)
•
••
•
Will also cover
(iv) Links between discrete & continuous Insurances
(e.g. using UDD
within each year of age)
(v) varying insurances(any type can have a varying benefit in theory)
(vi) Recursive formulas
(vii) Consideration of select rates
•
••
•
Lecture ordering of topics differ from text but all topics will be covered
This handout may require a few in class modifications to properly
reflect full notation
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AS2427 Chapter4 Lecture Notes – February 2018
3
)&&
•
Will assume (for Ch.4 & 5) a constant and fixed interest rate
•
Many Ch.4 text examples/exercises use the text
‘Standard
Ultimate Survival Model” introduced in 3.9
–
u
x
=
A+Bc
x
, where
A= 0.00022 B=2.7x10-6 and c =1.124
–
see Appendix D for selected values (plus posted excel WS)
•
••
• Many Theory of interest concepts(AS2553) used/built upon;
International actuarial notation(IAN) used in AS2553 is
expanded(for life annuities, and Life insurance)
Interest rate notation and equivalencies, such as;
e
t
= (1+i)
t
= (1+ i
(p)
/p)
pt
e
= v
= (1+i)
-1
and
= log(1+i)=ln(1+i)
e
t
= v
t
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