PDE for Finance Notes, Spring 2011 Section 9
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use only in
connection with the NYU course PDE for Finance, G63.2706. Prepared in 2003, minor
updates made in 2011.
Scope of the nal exam
Asset Price Bubbles from Heterogeneous Beliefs
about Mean Reversion Rates
Xi Chen and Robert V. Kohn
Courant Institute of Mathematical Sciences
New York University
[email protected], [email protected]
Corrected version, August 6, 2009
To appear in Finan
PDE for Finance Notes Stochastic Calculus Review
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use in connection with the NYU course PDE for Finance, G63.2706. Prepared in 2003, minor adjustments made 2011.
These notes provide a
PDE for Finance Notes, Spring 2003 Section 9
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use only in
connection with the NYU course PDE for Finance, G63.2706.
About the nal exam: As previously announced, our exam is Monday May
PDE for Finance Notes, Spring 2003 Section 8
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use only in
connection with the NYU course PDE for Finance, G63.2706.
Minor corrections and clarifications added 4/28/03.
Underlyings wit
PDE for Finance Notes, Spring 2003 Section 7
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use only in
connection with the NYU course PDE for Finance, G63.2706.
About the nal exam: Our exam is Monday May 12, 8-10pm, in the usual
PDE for Finance Notes, Spring 2003 Section 6
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use only in
connection with the NYU course PDE for Finance, G63.2706.
Optimal stopping and American options. Optimal stopping refers to a
PDE for Finance, Spring 2011 Homework 1
Distributed 1/24/2011, due 2/14/2011. HW must be turned in by the due date to get credit,
unless an extension has been granted.
1) Consider the lognormal random walk
dy = ydy + ydw
1
starting at y (0) = x. Assume =
PDE for Finance, Spring 2011 Homework 2
Distributed 2/14/11, due 2/28/11.
1) Consider the linear heat equation ut uxx = 0 in one space dimension, with discontinuous
initial data
0 if x < 0
u(x, 0) =
1 if x > 0.
(a) Show by evaluating the solution formula
PDE for Finance, Spring 2011 Homework 3
Distributed 2/28/11, due 3/21/11.
1) Consider the linear heat equation ut uxx = 0 on the interval 0 < x < 1, with boundary
condition u = 0 at x = 0, 1 and initial condition u = 1.
(a) Interpret u as the value of a s
PDE for Finance Notes, Spring 2011 Section 8
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use only in
connection with the NYU course PDE for Finance, G63.2706. Prepared in 2003, minor
updates made in 2011.
Underlyings with jump
PDE for Finance Notes, Spring 2011 Section 7
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use only in
connection with the NYU course PDE for Finance, G63.2706. Prepared in 2003, minor
updates made in 2011.
About the nal exam: O
PDE for Finance Notes, Spring 2011 Section 6
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use only in
connection with the NYU course PDE for Finance, G63.2706. Prepared in 2003, minor
updates made in 2011. Revised and extended
PDE for Finance Notes, Spring 2011 Section 5
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use only in
connection with the NYU course PDE for Finance, G63.2706, Prepared in 2003, minor
updates made in 2011.
Stochastic optimal co
PDE for Finance Notes, Spring 2011 Section 4
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use only in
connection with the NYU course PDE for Finance, G63.2706. Prepared in 2003, minor
updates made in 2011.
Deterministic optimal
PDE for Finance Notes, Spring 2011 Section 3.
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use in connection with the NYU course PDE for Finance, G63.2706. Prepared in 2003, minor updates
and corrections made in 2011.
More abou
PDE for Finance Notes, Spring 2011 Section 2.
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use in connection with the NYU course PDE for Finance, G63.2706. Prepared in 2003, minor updates
made in 2011.
Solution formulas for the
PDE for Finance Notes, Spring 2011 Section 1.
Notes by Robert V. Kohn, Courant Institute of Mathematical Sciences. For use in connection with the NYU course PDE for Finance, G63.2706. Prepared in 2003, minor updates
made in 2011.
Links between stochastic
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 stat
PDE for Finance, Spring 2011 Homework 5
Distributed 4/4/11, due 4/18/11.
Problem 1 is a classic example (due to Merton) of optimal asset allocation. Problems 2-4
reinforce our discussion of optimal stopping and American options.
1) Consider the following
PDE for Finance, Spring 2011 Homework 4
Distributed 3/21/11, due 4/4/11.
These problems concern deterministic optimal control (Section 4 material). Warning: some
of the problems here are a bit laborious (though they are not necessarily dicult).
1) Conside