the investor does not affect the evolution of the state variable zt. Equiva-
lently, the investor believes that his actions will have no impact on the fu-
ture evolution of zt. As we argued earlier, this is a reasonable assumption
for many actions the investor might take, but is less so in the case of a com-
plete exit from the stock market. In essence, our assumption means that the
investor does not consider using his cushion of prior gains in a strategic
fashion, perhaps by waiting for the cushion to become large, exiting from
the stock market so as to preserve the cushion and then reentering after a
market crash when expected returns are high.^19
B. Stock Prices in Economy IIIn Economy II, consumption and dividends follow distinct processes.
This allows us to model the stock for what it really is, namely a claim to
the dividend stream, rather than as a claim to consumption. Formally, we
assume
(29)and
(30)where
(31)This assumption, which makes log /Dta random walk, allows us to con-
struct a one-factor Markov equilibrium in which the risk-free interest rate
is constant and the price-dividend ratio of the stock is a function of the
state variable zt.^20 The stock return can then be written as
(32)Given that the consumption and dividend processes are different, we need
to complete the model specification by assuming that each agent also re-
ceives a stream of nonfinancial income {Yt}—labor income, say. We assume
Rfz
fz
t t e
tgDDt
+
= + + + +
11 () (^11)
()
.
σ
Ct
η
∼
ω
ω
t
t
N
i.i.d. , .
0
0
1
1
log(DD gtt D Dt++^11 / )=+σ ,
log(CC gtt C Ct++^11 / )=+ση,
PROSPECT THEORY AND ASSET PRICES 243
(^19) Allowing the investor to consider such strategies does not change the qualitative nature
of our results. It may affect our quantitative results depending on how one specifies the evolu-
tion of the investor’s cushion of prior gains after he leaves the stock market.
(^20) Another approach would model and Dtas cointegrated processes, but we would then
need at least one more factor to characterize equilibrium prices.
Ct