Psychological Aspects of Market Crashes

rules out the need for social coordination about the anticipation of the crash
(this can be regarded as implicitly assumed). The representative agent has
a utility function of the form

U(c) = E^{P   X} β^tu(ct) ,

t∈N+

where P is an arbitrary belief process, where β ∈ (0, 1) is a constant, and
where the function u is defined as
for some α > 0 (this parameter is the coefficient of risk-aversion of the agent).
We show in Appendix B that the asset structure is irrelevant to carry out
our simulations, provided that the agent is not constrained in borrowing in
equilibrium.

Fix now any history s_t-1, let s_t → s_t-1 be the history following s_t-1 where
the crash is expected and let st ,→ st-1 be the other history following st-1 .
In Appendix B, we show that

RSt ≤ ∣4∙( wwst- )^α                  (⁶)

^{β 1}St      wst-1

for every security j as before, and regardless of the asset structure provided
that the agent is not constraint in borrowing in equilibrium. In particular,
Inequality (6) shows that the upper-bound on equilibrium returns depends
only the parameters γ, δ, α and β . The following numerical simulations are
generated directly from this last inequality.

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