This carp was caught on a `halibut oil' pellet. The fish came from the
Monk Lake Fishery, Staplehurst, Kent.
Some of the material linked to this page arose from questions asked
by students as they struggled with their MSc course or their PhD
studies. It is, therefore, rather jumbled. Where possible, I've tried to
provide a commentary so you can see how the matter arose. Hopefully this
may spark a connection with your own work and perhaps be of value
there. If it does and you'd like to share this knowledge let me know and
I'll include a link to your work or make a file available on this site.
- Do Conditional Expectations Factorise?
This question arose when Alek Zupan asked if, for independent random
variables, the conditional expectation of a product was the product of
the conditional expectations. He was motivated by a problem in Credit
Risk and it might be worth mentioning that Estathious Margonis also
asked the same question in connection with a problem in Credit Risk. The
answer to the question is "no". However, one does get a kind of
factorisation of a conditional expectation when you have more than one
measure around! Specifically, a risk-nuetral measure and a forward
measure. I shall add a page relating to this as soon as I can.
- Remarks about the Black Scholes Formula
This is a presentation of the usual Black-Scholes theory for pricing a
call option. It also includes some material on portfolio management
which I will excise when I get round to it........
- Pricing a Sequential Option This
piece of work was generated by a question from Gerry Salkin. It takes
the form of a note to Gerry, I saw no reason to change this. There are
suggestions for extending the work described here in the text, it may be
that you have already done this. If so let me know.
- Some notes on stopping times This is the
usual introduction to Stopping Times. I'll develop the material in this
file, as time permits.
- A Martingale Representation Theorem
This looks at martingale representation for discrete time and finite
state space. There is a nice mixture of geometry and linear algebra in
this work. I wrote this, and you will see that it is hand written, by
way of explaining some the details of M. Dothan's book to someone. I
hope it can help you.
- Some notes on Swaps . This does the elementary stuff on swaps and swaptions.
- Lebesgue Integration and some Measure Theory This is an old fashioned approach to measure and integration on the real line. It's worth following through before taking a more economic approach, such as that in Walter Rudin's "Real and Complex Analysis"
- Back to the homepage
- Problems (and solutions) for Stochastic
- Research Interests
Department of Mathematics
London SW7 2AZ
My e-mail address