Solution for Homework 1. PDE for Finance, Spring 2012
These solutions are lightly edited versions of ones prepared by prior TA Fan-fu Feng.
1) Denote the generator of the lognormal process by L, i.e, Lu = xux + 1 2 x2 uxx .
2
(a) The equation Lu = 1 is an
Solution for Homework 6. PDE for Finance, Spring 2012
These solutions are lightly-edited versions of ones prepared by prior TA Fan-fu Feng.
1) (a) The HJB equation is
0 = ut + min Lu + running cost
= ut + min
= ut + min 2 + (p + up uw )
1
uw + up + 2 upp
Solution for Homework 5. PDE for Finance, Spring 2012
These solutions were prepared by Doris Dobi and Fan-fu Feng.
1) (a) The portfolio process is
dy = (1 )rydt + y (dt + dw) = [(1 )r + ]ydt + ydw
Thus the HJB equation for this control problem is
ut + max
Solution for Homework 4. PDE for Finance, Spring 2012
These solutions were prepared by Doris Dobi, Fan-fu Feng, and Juyoung Lim.
1) For notational convenience we use subscripts to denote partial derivatives. Note that
after the change of variables given i
Solution for Homework 3. PDE for Finance, Spring 2012
These solutions were prepared by Doris Dobi and Fan-fu Feng.
1) (a) u is the value of a knock-out double-barrier option that pays 1 if the underlying has
not yet hit either of the barriers.
4 n2 2 t
(b
Solution for Homework 2. PDE for Finance, Spring 2012
These solutions are lightly edited versions of ones prepared by prior TA Fan-fu Feng.
1) Recall the solution formula (2) in p.2 of section2 that says if a function u solves the heat
(y x)2
1
equation w
PDE for Finance, Spring 2012 Homework 6
Distributed 4/16/2012, due 4/30/2012.
No extensions. Reminder: nal exam on May 7th in class, usual place and time.
You may bring two sheets of notes (8.5 11, both sides, any font). The preparation
of such notes is a
PDE for Finance, Spring 2012 Homework 5
Distributed 4/9/2012, due 4/23/2012.
HW must be turned in by the due date to get credit, unless an extension has been granted.
Comment: this is similar to Bob Kohns homework from last year, so be vigilant with
respe
PDE for Finance, Spring 2012 Homework 4
Distributed 3/19/2012, due 4/9/2012.
There is no lecture next week (March 26)! Hence this homework is due in three
weeks instead of two.
HW must be turned in by the due date to get credit, unless an extension has be
PDE for Finance, Spring 2012 Homework 3
Distributed 2/27/2012, due 3/12/2012. HW must be turned in by the due date to get credit,
unless an extension has been granted.
Comment: this is similar to Bob Kohns homework from last year, so be vigilant with
resp
PDE for Finance, Spring 2012 Homework 2
Distributed 2/13/2012, due 2/27/2012. HW must be turned in by the due date to get
credit, unless an extension has been granted.
Comment: this is similar to Bob Kohns homework from last year, so be vigilant with
resp
PDE for Finance, Spring 2012 Homework 1
Distributed 1/23/2012, due 2/13/2012. This is three weeks, for the rest of the course
it will be two weeks. HW must be turned in by the due date to get credit, unless an
extension has been granted.
Comment: this rst