... are supported by
recent empirical findings reported by Finkelstein and Poterba (20 02,
20 04), who studied the U.K. annuity market. In a pioneering paper
(Finklestein and Poterba, 20 04), they test ... that from (11.19)–(11 .21 ), it follows that
p
a
< p
x
a
< p
a
+ δ (11 .22 )
is a necessary condition for an interior solution. When the left-hand-side
inequality in (11 .22 ) does n...
... − p
α
2
(1 − e
−α
2
(R
∗
−M)
)
1
α
(e
αM
− 1) +
p
α
1
+
1 − p
α
2
.
(8.31)
August 20 , 20 07 Time: 05:47pm chapter08.tex
64
•
Chapter 8
Now let
r(z) =
pF
1
(z)r
1
(z) + (1 − p)F
2
(z)r
2
(z)
pF
1
(z) ... following conclu-
sion: The unique solution to (8 .22 ) and (8 .23 ) that satisfies (8.1), with
r(z) given by (8 .25 ), is c = c
1
= c
2
= c
∗
and R
∗
1
= R
∗
2
= R
∗
, whe...
... exists an age z
c
,
0 < z
c
< T, such that (figure 3 .2)
F
1
(z)
T
0
F
1
(z) dz
F
2
(z)
T
0
F
2
(z) dz
as z z
c
. (3.4)
August 22 , 20 07 Time: 09:50am chapter01.tex
8
•
Chapter 1
equilibrium ... 31, 20 07 Time: 03:51pm chapter 02. tex
Benchmark Calculations
•
13
Table 2. 1
Consumption, Savings, and Wealth at Retirement.
ρ =
1
2
ρ =
2
3
M = 0 M = 5 M = 0 M = 5
c .89...
... and ρ = δ>0. From (5 .20 ) and (5 .21 ), R
∗
is then determined by the condition
u
w(1 − e
−ρ R
∗
)
1 − e
−ρT
w = e
(5 .25 )
August 20 , 20 07 Time: 05:46pm chapter04.tex
22
•
Chapter 4
Figure ... independent survival probability, p. The couple maximizes the
family’s expected utility, 2V
c
= 2u(c
0
) + 2p
2
u(c
1
/2) + 2p(1 − p)u(c
1
),
where c
0
is per-capita consumption in...
... q
1
1
and q
2
1
and on
˜
y
1
1
(p) and
˜
y
2
1
(p), defined above. Thus, the existence and uniqueness of (
ˆ
q
1
1
,
ˆ
q
2
1
),
defined by (16 .20 ) and (16 .21 ), requires certain conditions.
From (16 .21 ) ... (
ˆ
q
1
1
,
ˆ
q
2
1
), are defined by zero expected profits
conditions
¯
p
p
(
ˆ
q
1
1
− p)
ˆ
a
1
(p, ·) dF( p) = 0 (16 .21 )
and
¯
p
p
(
ˆ
q
2
1
− p)
ˆ
b
1
(p, ·) dF( p...