Psychological Aspects of Market Crashes

system of asset prices q, define first the return of tree j (j = 1, ..., J) in
history st+1, when purchased in history st, as
if q_s^j_t > 0, and arbitrarily otherwise. With this notion, we can describe our
notion of market crash.

Definition 2 For every ε > 0, an ε-crash occurs in history s_t if R^j_st < ε for
every asset j such that d^j_st > 0.

A market crash in a given history is thus defined as an arbitrarily low
return on every asset paying off strictly positive dividend in this history. In
the remainder of the paper, we are primarily interested in finding conditions
leading to arbitrarily low market crashes. In particular, we analyze how
individual anticipations of variations in market fundamentals can generate
crashes as described above.

3 Beliefs and market crashes

In this section, we study how market crashes are linked to anticipations of
variations in aggregate endowment, and what level of social coordination
about the anticipations is needed for a crash to occur.. Our result gives a
set of sufficient conditions on beliefs and aggregate endowments leading to
arbitrarily low market crashes.

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