The Information Efficiency of Stock Markets - Innovative Management in Information and Production - page 204

( Ω , )

denote that the
information source of stock markets is open for all market participants (information
users). The process of market participants' observing signal

In sense of information theory, above assumptions on P

ϕ ( ω )=

∈

S is an
information transmission and reception process. The process of market participants'
assigning state

s

( ω | )

ω with a posteriori probability P s is an information judging

process.

3 Information Efficiency of Stock Markets

To improve the information efficiency of stock markets, we should let the prices of
stock fully reflect all information related to pricing and guide investors to reasonably
anticipate relevant information, so that stocks' prices can dynamically approach to
their intrinsic values. Here the stock's price is one of the observed signals and the
stock's intrinsic value is determined by the natural state. If the observed stock price
accurately reflects information of the natural state, it faithfully reflects the intrinsic
value of the stock. Based on this idea, we redefine information efficiency of stock
market based on our definition of information in Sect. 2 .
Assume

the set of stock market participants is N ,s . | N | = n .For

participant i ∈ N ,let S i , ϕ i and d i separately denote its signal type set,

n

signal mapping, and coincidence degree. Define S = Π

i = 1 (

S i ) with its member

s =( s 1 , s 2 ,··· , s n ) ∈ S ,where s i ∈ S i , i = 1 , 2 ,···, n . Hence, for ( ω , s ) ∈ Ω × S ,

d ( ω , s )=( d 1 ( ω , s 1 ) , d 2 ( ω , s 2 ) ,··· , d n ( ω , s n )) .

R n and f is a strictly monotonically increasing
continuous function determined by information transmission mechanism of market
on B :

n

Assume B = Π

i = 1 [ −

1 , 1 ] ⊂

f : B → R , y = f ( x 1 , x 2 ,···, x n ) s . t .| f ( x ) |≤ 1 ,∀ x ∈ B (3)

Let D denote completeness degree of information in the stock market. D can be
determined by following mapping:

F : Ω × S → R ,

(4)

D = F ( ω , s )= f ( d ( ω , s )) = f (( d 1 ( ω , s 1 ) , d 2 ( ω , s 2 ) ,···, d n ( ω , s n )))

Because of the strict monotone of f , the stronger information on natural state
{ ω }

signal s conveys, i.e., the better consistency between signal ϕ ( ω )= s and

natural state { ω } , the greater is the completeness degree of information in the stock

market.
Assume value range of f is R f and g is a strictly increasing continuous function
determined by operation mechanism of market on R f

g : R f → R , z = g ( y ) , s . t | g ( y ) |≤ 1 ,∀ y ∈ R f (5)