The Economic Theory of Annuities 1 pptx
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...
The Economic Theory of Annuities by Eytan Sheshinski_6 pdf
... 2p
2
u(c
1
/2) + 2p (1 − p)u(c
1
),
where c
0
is per-capita consumption in the first period and c
1
is total
consumption in the second period. The second term is the sum of the
expected utilities of ... dz
T
0
exp
−
z
0
1
σ
f (x)
F (x)
dx
dz
(5.33)
Optimum consumption decreases with age, its rate of decline being
equal to the product of the inverse of...
The Economic Theory of Annuities by Eytan Sheshinski_8 potx
... 0,
ˆ
a
1
= 0, p ≤ p < p
b
.
(16 .14 )
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
− ... ϕ(q
1
1
) strictly increases for all
q
1
1
, E( p) < q
1
1
< p. From (16 A.6), the condition is
ϕ
(q
1
1
) =
p
p
a
ˆ
a
1
(p) + (
ˆ
q
1
1
− p)
d
ˆ
a...
The Economic Theory of Annuities_1 pptx
... Pricing of Annuities 11 3
Appendix 11 6
Chapter 14
Optimum Taxation in Pooling Equilibria 11 8
14 .1 Introduction 11 8
14 .2 Equilibrium with Asymmetric Information 11 9
14 .3 Optimum Commodity Taxation 12 2
14 .4 ... Taxation 12 2
14 .4 Optimum Taxation of Annuities 12 5
Appendix 12 9
Chapter 15
Bundling of Annuities and Other Insurance Products 13 1
15 .1 I...
The Economic Theory of Annuities_2 pptx
... 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 =
λ
1 + λ
1
ˆ
X − 1
ˆ
K.
(14 .20)
Equation ... ε
11
=
ˆ
q
a
s
11
/
ˆ
a,
ε
12
=
ˆ
q
a
s
12
/
ˆ
a, ε
21
=
ˆ
q
b
s
21
/
ˆ
b, ε
22
=
ˆ
q
b
s
22
/
ˆ
b:
ε
11
ˆ
t
a
+ ε
12
ˆ
t
b
=−θ −
ˆ...
The Economic Theory of Annuities_10 pptx
... and, 11 8, 12 4–25, 12 7; rate
of return and, 71; stability and, 12 9;
uniqueness and, 12 9; welfare function
and, 12 0
August 18 , 2007 Time: 11 :35am index.tex
15 8
•
Index
Brugiavini, A., 82n26, 13 6, 14 2n 51
bundling, ... Hall.
Rabin, M. 19 98. Psychology and economics. Journal of Economic Literature
36: 11 –46.
Ramsey, F. P. 19 27. A contribution to the theory...
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
>...
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