hw6 (2)

# hw6 (2) - PDE for Finance Spring 2011 – Homework 6...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PDE for Finance, Spring 2011 – Homework 6 Distributed 4/18/11, due 5/2/11 . No extensions! 1) This problem develops a continuous-time analogue of the simple Bertsimas & Lo model of “Optimal control of execution costs” presented in the Section 7 notes. The state is ( w,p ), where w is the number of shares yet to be purchased and p is the current price per share. The control α ( s ) is the rate at which shares are purchased. The state equation is: dw =- αds for t < s < T, w ( t ) = w dp = θαds + σdz for t < s < T, p ( t ) = p where dz is Brownian motion and θ , σ are fixed constants. The goal is to minimize, among (nonanticipating) controls α ( s ), the expected cost E ( Z T t [ p ( s ) α ( s ) + θα 2 ( s )] ds + [ p ( T ) w ( T ) + θw 2 ( T )] ) . The optimal expected cost is the value function u ( w ,p ,t ). (a) Show that the HJB equation for u is u t + H ( u w ,u p ,p ) + σ 2 2 u pp = 0 for t < T , with Hamiltonian H ( u w ,u p ,p ) =- 1 4 θ ( p + θu p- u w ) 2 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

hw6 (2) - PDE for Finance Spring 2011 – Homework 6...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online