what constitutes a reasonable value for b 0 and so present results for a range
of values.^25
The two final parameters, ηand , arise in the definition of the state
variable dynamics. is not a parameter we have any control over: it is
completely determined by the other parameters andthe requirement that
the equilibrium median value of ztbe equal to one. The variable ηcontrols
the persistence of ztand hence also the persistence of the price/dividend ratio.
We find that an ηof 0.9 brings the autocorrelation of the price/dividend ratio
that we generate close to its empirical value.

B. Methodology

Before presenting our results, we briefly describe the way they were ob-
tained. The identical technique is used for both Economy I and II, so we de-
scribe it only for the case of Economy I. The difficulty in solving equation
(24) comes from the fact that zt+ 1 is a function of both
t+ 1 and f(⋅). In eco-
nomic terms, our state variable is endogenous: it tracks prior gains and
losses, which depend on past returns, themselves endogenous. Equation
(24) is therefore self-referential and needs to be solved in conjunction with

(35)

and

(36)

We use the following technique. We start out by guessing a solution to
(24), f(0)say. We then construct a function h(0)so that zt+ 1 =h(0)(zt,
t+ 1 )
solves equations (35) and (36) for this f=f(0). The function h(0)determines
the distribution of zt+ 1 conditional on zt.
Given the function h(0), we get a new candidate solution f(1)through the
following recursion:

(37)

1

1

1

1

1

1

0

1

1

1

1

=

 +















+

 +



























∀

+

+

−+

+

+

+

+

+

ρΕ

ρΕ

γσ

t

i

t

i

t

g

t

i

t

i

t

g

tt

fz

fz

e

bv

fz

fz

ezz

CCt

CCt

()

()

()( )

()

()

()

()

ˆ ()

()

,,.

σ

R

fz

fz

t t e

t

gCCt

+

= + + + +

1

1 () (^11)
()
σ
.
zz
R
tt+ Rt+






1 +−
1
ηη()(), 11
R
R
PROSPECT THEORY AND ASSET PRICES 249
(^25) One way to think about b 0 is to compare the disutility of losing a dollar in the stock mar-
ket with the disutility of having to consume a dollar less. When computed at equilibrium, the
ratio of these two quantities equals b 0 ρλ. By plugging numbers into this expression, we can see
how b 0 controls the relative importance of consumption utility and nonconsumption utility.