Liquidity modelling
There is a demandDfor liquid resources, cash or euro in a bank or in a
teller machine, with distribution functionF.There are two costs:his the
holding cost andpis the penalty for not satisfying the demand. What is
the level of optimal supplyS?Our goal function is
J(S)=hE
(S D)+
+pE
(D S)+
.
If there is a density function then
E
(D S)+
=
Zā
S
(x S)f(x)dx
E
(S D)+
=
Z
R
(S x)+dF(x)=
Z
R
(S x)+f(x)dx=
=
ZS
0
(S x)f(x)dx.