Psychological Aspects of Market Crashes



the analysis, we assume that Pst > 0 for every history st .

To conclude this section, we define the operators EQ to be the expectation
operator associated with
Q. Finally, we say that a finite history st+p St+p
follows a finite history st St (t, p N), denoted by st+p ,→ st, if there
exists
s Sp such that st+p = (st, s).

2.1 The agents

In this section, economic agents are described. There is a finite number I ≥ 1
of infinitely-lived agents behaving competitively.

There is a single consumption good available in every period t (t N+).
Denote by cist the consumption of an agent i (i = 1, ..., I) in history st St
(t N+). In every period t (t N+) and in every history st St, every
agent
i (i = 1, ..., I) is endowed with wsit > 0 units of consumption goods.

In every period t N , and after the realization of the history st St , the
agents trade
L ≥ 1 infinitely-lived assets, or Lucas’ trees as in Lucas (1978).
Every tree
j (j = 1, ..., L) yields a dividend djst > 0 of units of consumption
good in history
st. Let dst denote the vector (ds1t, ..., dsLt) for every st. The
supply of every tree is assumed to be 1 in every history.

The aggregate endowment wst , in every history st (st St and t N+),
is given by

wst = i wsit + j djst .

The price in history st of one share of the tree j (1 ≤ j ≤ L) is denoted
by
qsjt , for every st St and t N+. Let qst denote the vector (qs1t , ..., qsLt)



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