Mathematics for Economists

Liquidity modelling

Hence

J(S)=h

ZS

0

(Sx)f(x)dx+p

Z∞

S

(xS)f(x)dx.

Using the formula

d

dx

Zφ 2 (x)

φ 1 (x)

f(x,y)dy = f(x,φ 2 (x))φ^02 (x)

f(x,φ 1 (x))φ^01 (x)+

+

Zφ 2 (x)

φ 1 (x)

∂

∂xf(x,y)dy

dJ

dS = h(SS)+h

ZS

0

1 
f(x)dx+

p(SS)+p

Z∞

S

 1 
f(x)dx.