Review of The Economic Theory of Annuities 1 potx
Review of The Economic Theory of Annuities_1 potx
... chapter14.tex
12 4
•
Chapter 14
Rewrite (14 .19 ) in the more familiar form:
ˆ
tS =−
1
1 + λ
1( λ
ˆ
X +
ˆ
K
ˆ
Q)
ˆ
Q
1
,
and substituting from (14 .15 ),
ˆ
tS =
λ
1 + λ
1
ˆ
X − 1
ˆ
K.
(14 .20)
Equation ... 1. The indirect utility,
ˆ
u,is
therefore
ˆ
u(p
1
, p
2
; α) = ln
α
p
1
α
1 − α
p
2
1 α
+ R − 1.
(15 .3)
August 18 , 2007 Time: 11 :22am chap...
Review of The Economic Theory of Annuities_4 ppt
... 0.005 216 0.009766
10 7 0.000 311 0.0 013 94 0.00 318 9 0.006259
10 8 0.00 017 5 0.000 813 0.0 018 30 0.003784
10 9 0.000094 0.000455 0.000974 0.00 213 1
11 0 0.000049 0.000244 0.000473 0.0 011 00
11 1 0.000025 0.00 012 5 ... 0.074 510 0 .16 5364 0 .18 3735 0.260889
94 0.057496 0 .13 46 41 0 .15 5093 0.222355
95 0.043497 0 .10 7438 0 .12 9260 0 .18 7020
96 0.032263 0.084 018 0 .10 6332...
Review of The Economic Theory of Annuities_6 potx
... total
consumption in the second period. The second term is the sum of the
expected utilities of two surviving individuals, while the third is the
expected utility of one survivor. The budget constraint ... Annuitization
Suppose that the individual can purchase or sell at any age an asset called
annuities. The quantity of annuities at age z is denoted a(z). A unit...
Review of The Economic Theory of Annuities_7 doc
... .11 .32 .14 .34
W 5.37 10 .14 6. 91 11. 31
The values chosen for ρ take into account that social security (SS)
benefits provide (in the United States) a replacement ratio of 25–30
percent for the average ... 20 01, chap. 2). The growth of individual annuities has
exceeded that of group annuities, reflecting the decline in defined benefits
pension plans and the rapid expans...
Review of The Economic Theory of Annuities_8 pptx
... y
1
<
˜
y
1
1
(p) (see figure 16 .1) .
August 18 , 2007 Time: 11 :25am chapter16.tex
Chapter 16
•
15 1
Denote by ϕ expected profits in the period -1 market for annuities,
ϕ(q
1
1
) =
p
p
a
(q
1
1
− ... q
2
1
b
1
)q
1
1
+ pu
(a
0
− b
1
) > 0 for all y
1
>
˜
y
1
1
(p) and b
1
≥ 0, it follows
that
ˆ
a
1
(p, y
1
) > 0 for all
¯
y
1
≥ y
1
>...
Review of The Economic Theory of Annuities_9 pot
... Press.
Mirrlees, J. A. 19 71. An exploration in the theory of optimum income taxation.
Review of Economic Studies 38(2): 17 5–208.
August 18 , 2007 Time: 11 :35am index.tex
Index
•
16 1
population theory: aggregate ... timing of
purchases and, 13 5
Utkus, Stephen, 14 8
August 18 , 2007 Time: 11 :35am index.tex
15 8
•
Index
Brugiavini, A., 82n26, 13 6, 14 2n 51
bund...
The Economic Theory of Annuities by Eytan Sheshinski_1 pdf
... the following.
August 18 , 2007 Time: 11 :22am chapter14.tex
12 4
•
Chapter 14
Rewrite (14 .19 ) in the more familiar form:
ˆ
tS =−
1
1 + λ
1( λ
ˆ
X +
ˆ
K
ˆ
Q)
ˆ
Q
1
,
and substituting from (14 .15 ),
ˆ
tS ... = R − 1. The indirect utility,
ˆ
u,is
therefore
ˆ
u(p
1
, p
2
; α) = ln
α
p
1
α
1 − α
p
2
1 α
+ R − 1.
(15 .3)
August 18 , 2007 Time: 11 :22...
The Economic Theory of Annuities by Eytan Sheshinski_3 ppt
... associated with (11 .18 ). Equations
(11 .18 )– (11 . 21) jointly determine positive amounts
ˆ
a( p
a
, p
x
a
; α),
ˆ
a
x
(p
a
, p
x
a
; α), and
ˆ
b(p
a
, p
x
a
; α).
Note first that from (11 .19 )– (11 . 21) , it follows ... dG(α)
(11 .28)
August 18 , 2007 Time: 10 :40am chapter 11. tex
86
•
Chapter 11
To see this, observe that the solution
ˆ
p
a
and
ˆ
p
b
= 1 satisfying (11 .6)
and...
The Economic Theory of Annuities by Eytan Sheshinski_4 ppt
... 0.0009 01 0.003699 0.008094 0. 014 519
10 6 0.000538 0.002309 0.005 216 0.009766
10 7 0.000 311 0.0 013 94 0.00 318 9 0.006259
10 8 0.00 017 5 0.000 813 0.0 018 30 0.003784
10 9 0.000094 0.000455 0.000974 0.00 213 1
11 0 ... 0.000473 0.0 011 00
11 1 0.000025 0.00 012 5 0.000206 0.000 510
11 2 0.000 012 0.0000 61 0.000078 0.000206
11 3 0.000005 0.000028 0.000024 0.000068
11 4 0.0000...
The Economic Theory of Annuities by Eytan Sheshinski_5 doc
... because the
annuities held by individuals in this class are worth more because of the
5
The change in r(z)is
˙
r(z) =
δr
1
δr
1
+ (1 − δ)r
2
f
1
(z)
f
1
(z)
+
(1 − δ)r
2
δr
1
+ (1 − δ)r
2
f
2
(z)
f
2
(z)
.
The ... interest on assets, the competitive rate
of return on annuities is equal to the rate of interest plus the hazard rate.
The reason...
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