Psychological Aspects of Market Crashes

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

To conclude this section, we define the operators E^Q to be the expectation
operator associated with Q. Finally, we say that a finite history s_t+p ∈ S^t+p
follows a finite history st ∈ S^t (t, p ∈ N), denoted by st+p ,→ st, if there
exists s ∈ S^p 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 cⁱ_st the consumption of an agent i (i = 1, ..., I) in history s_t ∈ S^t
(t ∈ N+). In every period t (t ∈ N+) and in every history st ∈ S^t, every
agent i (i = 1, ..., I) is endowed with w_sⁱ_t > 0 units of consumption goods.

In every period t ∈ N , and after the realization of the history s_t ∈ S^t , the
agents trade L ≥ 1 infinitely-lived assets, or Lucas’ trees as in Lucas (1978).
Every tree j (j = 1, ..., L) yields a dividend d^j_st > 0 of units of consumption
good in history s_t. Let d_st denote the vector (d_s¹_t, ..., d_s^L_t) for every s_t. The
supply of every tree is assumed to be 1 in every history.

The aggregate endowment ws_t , in every history st (st ∈ S^t and t ∈ N+),
is given by

wst = _i wsⁱ_t + _j d^js_t .

The price in history st of one share of the tree j (1 ≤ j ≤ L) is denoted
by q_s^j_t , for every st ∈ S^t and t ∈ N+. Let qs_t denote the vector (q_s¹_t , ..., q_s^L_t)

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