<s>
The	O
seven	B-Algorithm
states	I-Algorithm
of	I-Algorithm
randomness	I-Algorithm
in	O
probability	O
theory	O
,	O
fractals	B-Application
and	O
risk	O
analysis	O
are	O
extensions	O
of	O
the	O
concept	O
of	O
randomness	O
as	O
modeled	O
by	O
the	O
normal	O
distribution	O
.	O
</s>
<s>
These	O
seven	O
states	O
were	O
first	O
introduced	O
by	O
Benoît	O
Mandelbrot	O
in	O
his	O
1997	O
book	O
Fractals	B-Application
and	O
Scaling	O
in	O
Finance	O
,	O
which	O
applied	O
fractal	B-Application
analysis	O
to	O
the	O
study	O
of	O
risk	O
and	O
randomness	O
.	O
</s>
<s>
The	O
importance	O
of	O
seven	B-Algorithm
states	I-Algorithm
of	I-Algorithm
randomness	I-Algorithm
classification	O
for	O
mathematical	O
finance	O
is	O
that	O
methods	O
such	O
as	O
Markowitz	O
mean	O
variance	O
portfolio	O
and	O
Black	O
–	O
Scholes	O
model	O
may	O
be	O
invalidated	O
as	O
the	O
tails	O
of	O
the	O
distribution	O
of	O
returns	O
are	O
fattened	O
:	O
the	O
former	O
relies	O
on	O
finite	O
standard	B-General_Concept
deviation	I-General_Concept
(	O
volatility	O
)	O
and	O
stability	O
of	O
correlation	O
,	O
while	O
the	O
latter	O
is	O
constructed	O
upon	O
Brownian	O
motion	O
.	O
</s>
<s>
The	O
classification	O
was	O
formally	O
introduced	O
in	O
his	O
1997	O
book	O
Fractals	B-Application
and	O
Scaling	O
in	O
Finance	O
,	O
as	O
a	O
way	O
to	O
bring	O
insight	O
into	O
the	O
three	O
main	O
states	O
of	O
randomness	O
:	O
mild	O
,	O
slow	O
,	O
and	O
wild	O
.	O
</s>
