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Paul
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Re: PWOQF, expected hitting time

May 28th, 2021, 2:53 am

Don't be cheeky, boy at the back!
 
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Cuchulainn
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Re: PWOQF, expected hitting time

May 28th, 2021, 9:37 am

The main thing is have you understood where the integral comes from and how that integration by parts was achieved?
Yes. Yes, I do.
Come to the blackboard Master Jones and solve the equation, step by step.
 
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Cuchulainn
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Re: PWOQF, expected hitting time

May 30th, 2021, 12:42 pm

From BS to heat Pde

https://www.math.tamu.edu/~stecher/425/ ... uation.pdf

on the 2nd line stating upfront that [$]V(0,t) = 0[$] is so wrong.
 
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bearish
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Re: PWOQF, expected hitting time

May 30th, 2021, 1:26 pm

From BS to heat Pde

https://www.math.tamu.edu/~stecher/425/ ... uation.pdf

on the 2nd line stating upfront that [$]V(0,t) = 0[$] is so wrong.

What have we here, laddie? Mysterious scribblings? A secret code? Three pages later we encounter an answer that is off by an odd factor of [$] e^{ \frac{\sigma^2}{8}} [$]. To a problem that would generously take two lines to answer with a probabilistic approach.
 
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Cuchulainn
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Re: PWOQF, expected hitting time

May 30th, 2021, 4:26 pm

I think Einstein pipped you at the post

http://stat.math.uregina.ca/~kozdron/Re ... and_BM.pdf
 
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bearish
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Re: PWOQF, expected hitting time

May 30th, 2021, 7:19 pm

I think Einstein pipped you at the post

http://stat.math.uregina.ca/~kozdron/Re ... and_BM.pdf
The author seems not to be aware of Bachelier. But it is inconvenient that the mathematical object of Brownian motion was first developed in the context of option pricing.
 
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Paul
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Joined: July 20th, 2001, 3:28 pm

Re: PWOQF, expected hitting time

May 30th, 2021, 8:19 pm

From BS to heat Pde

https://www.math.tamu.edu/~stecher/425/ ... uation.pdf

on the 2nd line stating upfront that [$]V(0,t) = 0[$] is so wrong.

What have we here, laddie? Mysterious scribblings? A secret code? Three pages later we encounter an answer that is off by an odd factor of [$] e^{ \frac{\sigma^2}{8}} [$]. To a problem that would generously take two lines to answer with a probabilistic approach.
Two or three lines? I'd like to see them. And no more copying from other boys' work this time! 
 
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Cuchulainn
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Re: PWOQF, expected hitting time

May 30th, 2021, 8:36 pm

From BS to heat Pde

https://www.math.tamu.edu/~stecher/425/ ... uation.pdf

on the 2nd line stating upfront that [$]V(0,t) = 0[$] is so wrong.

What have we here, laddie? Mysterious scribblings? A secret code? Three pages later we encounter an answer that is off by an odd factor of [$] e^{ \frac{\sigma^2}{8}} [$]. To a problem that would generously take two lines to answer with a probabilistic approach.
Two or three lines? I'd like to see them. And no more copying from other boys' work this time! 
I second that. Just make sure he does his 3rd conjugation Latin verbs as well.
 
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Paul
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Re: PWOQF, expected hitting time

May 30th, 2021, 9:14 pm

Yes. Give any of these so-called "Masters" a question that hasn't been on a past paper and they burst into tears. Even the swotty French exchange student on the front row thinks he's fooling us with his arrogance and body odour.
 
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Cuchulainn
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Re: PWOQF, expected hitting time

May 30th, 2021, 10:13 pm

And the Russians want you to solve the heat equation for them in Excel macros with dinky colours.
 
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Alan
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Re: PWOQF, expected hitting time

May 30th, 2021, 11:08 pm

bearish is correct. It's a two-liner at best:
Line 1: from the BS formula under std notation, it is immediate that [$]C_K = -e^{-r T} \Phi(d_2(K)) = -e^{-r T} E[1_{S_T>K}][$].
Line 2: The problem at hand is [$]3 e^{-r T} (E[1_{S_T>1}] - E[1_{S_T>2}]) =3  e^{-r T} ( \Phi(d_2(1)) -   \Phi(d_2(2)))[$]

page 3 of the link contain two typos.
 
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Cuchulainn
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Re: PWOQF, expected hitting time

May 31st, 2021, 4:03 pm

bearish is correct. It's a two-liner at best:
Line 1: from the BS formula under std notation, it is immediate that [$]C_K = -e^{-r T} \Phi(d_2(K)) = -e^{-r T} E[1_{S_T>K}][$].
Line 2: The problem at hand is [$]3 e^{-r T} (E[1_{S_T>1}] - E[1_{S_T>2}]) =3  e^{-r T} ( \Phi(d_2(1)) -   \Phi(d_2(2)))[$]

page 3 of the link contain two typos.
That note had two parts

1. transformation to heat equation with transition density/integral.
2. an example; the answer is based on the pde formula; anyone can do that :-)

Is there another way?

Naughty tutor Math 425.
 
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Alan
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Re: PWOQF, expected hitting time

May 31st, 2021, 8:01 pm

Probabilistic thinking in finance is an example of the Sapir-Whorf Hypothesis. 
 
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Cuchulainn
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Re: PWOQF, expected hitting time

July 8th, 2021, 1:17 pm

Probabilistic thinking in finance is an example of the Sapir-Whorf Hypothesis. 
Only saw this now.
I wonder how the Hopi tribe of Arizona would view first hitting time seeing that they have no words for time, past, present or future.
 
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Alan
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Re: PWOQF, expected hitting time

July 8th, 2021, 2:02 pm

Probabilistic thinking in finance is an example of the Sapir-Whorf Hypothesis. 
Only saw this now.
I wonder how the Hopi tribe of Arizona would view first hitting time seeing that they have no words for time, past, present or future.
Sounds like an excellent place to take out a 20-year loan!