Mathematics for Economists

Liquidity modelling

Theorem

If p>c,then there is an optimal strategy vsuch that

v(x)=



Sx if xS

0 if x>S.

The optimal value of SsatisÖes:

F(S)= 1 F(S)=c(^1 β)+βh

pβc+βh

.

That is

F(S)= pc

p+β(hc)

.

Compare with the static solution

F(S)=

pc

p+h.