Lowyat.NET: Latest topics by RyukA

Black Scholes derivation via Martingales.

RyukA — Tue, 16 Oct 2012 20:19:14 +0800

Hi All,

I am required to present a short seminar on Stochastic Calculus & Brownian Motion
to a small panel of mathematicians & classmates, as part of assessment.

However, my part is to talk about derivation of Black Scholes pricing formula ( PDE),
possibly from 2 approaches:
1. Ito's formulation, Feynman Kac formula etc.
2. Martingale Approach, (Girsanov's theorem)

However I have yet to learn continuous financial models, and have limited understanding on P,Q measures.
At the same time, I am afraid that too much finance terminology might be a problem esp. when it
is a math seminar where things have to kept in a really rigorous sense
(someone might ask how do I mathematically define a Self-financing Portfolio, or Risk neutral measure, which I dont want to go through heaps of proofs due to limited time)

In respect to the martingale approach, is there a way to derive the BS formula without going through too
much financial terminology while keeping the mathematics working?
Google present me a majority papers which is more towards finance, and hence it gets complicated with jargons.

It will be much helpful if someone can outline me a good site to get a more general proof, or some key ideas (theorems) that can do the trick.

Any feedback is much helpful.

Problem: Academic Referees

RyukA — Wed, 08 Aug 2012 16:31:48 +0800

Hi All,

Recently receive calls & emails from a few universities, asking for Academic referee and referral reports.

Ironically, I know its quite common for graduate research programs, but I am applying coursework programs in most of em.

In reference to that. I have a few questions, and wish anyone with similar experience or have an idea of how things work, to kindly provide their response:

1. what is the difference between testimonial by Academic referee vs Referral Report?

2. What are the common criteria/content such report should include, if the referee choose to personally "write" one?
formats?

3. Can an academics that have not supervised nor taught the applicant, be nominated as referee?

4. On a preference basis, is it more preferrable to get lecturers or academics with strong authority role (sub-dean, Director of education) as academic referees or would it be better for it to be lecturers in that "specific field" you want to pursue into. Pros and cons?

5. Again, on personal experience, are these reports really that important? how would one comment on the effectiveness of an academic referees' background, the report on supporting the postgraduate application?

*Considering I am a Credit Average applicant*

Thanks alot.

Some SPM level Probability Problems

RyukA — Mon, 31 Oct 2011 19:38:26 +0800

This is a small study concerning Mathematics education in High School context, in the scope of Probability & Stat.

For Students currently in SPM, PMR, or Pre-U,
are encouraged to answer the below 3 questions:

Q1. John have a box of 1000 balls. Of which, they can either be Blue, Red or Green.
He draw 10 balls, he got 3 blue, 3 Green, and 4 red. Then he put them back.
But he doesnt know the proportion of each type of ball. He drawn 500 out of it.
He observe 100Blue, 200 Red and 200Green.
He's about to draw the 501 th ball, what is the probability that the ball he drawn is not blue?

Q2. Lisa was doing a True-false quiz. when she stumbled upon the 10th question, which she cant decide.
she then asked the class of 50 students to respond their answer. Without prior information of what's the answer that the smart students gave,
she had 18 True, 32 False.
She answered "false" for question 10, what is the probability that she get full marks for her paper?

Advanced:
Q3. Mr. Smith created a generator. it generates 2 real-valued integer (number):
X: an integer that is positive. (0,1,2,....)
Y: an integer that is negative (0,-1,-2,-3,...)
Mr. Smith is interested to know and recruit data regarding the sum of both values,
what is the probability that the sum (X+Y) equals to zero?

for all those that answered, please state whether you are PMR( if you feel like doing it), SPM, Pre-U
and also provide brief calculations and/or reasoning to your solutions.
I am more concerned with reasoning and explanation, than just a figure.

Thank you for your time.
Dont be too concerned about others' answers. You never know who's right!

Additionally:
I am keen to receive comments by those currently working in Education, Tutoring, and Academics
in the field of Mathematics & statistics (of all levels). Explaining their choice on the poll, with a strong concern to
public education in this field.Neither the less, everyone from different disciplines are encouraged to drop a comment, if interested.
For those interested to talk about this, this thread can serve as a medium for discussion.

Polling:
Everyone is welcomed to vote on the polls.
the poll can be found here:
http://forum.lowyat.net/topic/2088869

Probability & Statistics on High school level

RyukA — Sun, 30 Oct 2011 00:56:52 +0800

This thread will serve as the medium for a majority of input and discussions.
http://forum.lowyat.net/topic/2090928

Here is just for the polling. Thanks!

[addedon]October 31, 2011, 5:53 am[/addedon]For those doing Pre-U, are encouraged to participate in this small study as well. cheers