Mathematics for Economists

Liquidity modelling

Example

Let the distribution ofDexponential withλ= 2 .Let the penaltyp= 3

and the holding costh=5 and letc= 1 .In the static model

F(S) = 1 exp( 2 S)=

3 1

3 + 5 =

2

8 =

1

4.

exp( 2 S) =

3

4 ,S

=^1

2 log



3

4



= 0 ,143 84.

Now letβ= 1 / 2 .In this case

F(S) = 1 exp( 2 S)=

3 1

3 +^12 ( 5 1 )

=

2

5.

exp( 2 S) =^3

5

,S=^1

2

log



3

5



= 0 ,255 41