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Paul
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Is the type of mathematics found in finance limited?

July 11th, 2018, 5:49 am

The questions means at least two things: Do we only see the same maths over and over again? If so, why?

My maths background is as a modeller. You will see from my papers that I have worked on many different areas of applied/industrial/applicable maths: I turn physical/financial processes into some math model for the obvious reasons. I have complained for decades about the state of modelling in finance. I see the same model over and over again, with little variation. When there is variation it is not generally liked by the majority of the community. And obviously I've complained about the accuracy of these models as well. 

What maths do we see? Martingales, Monte Carlo simulations, and the same linear diffusion equation, with the occasional trivial integral equation. Ad nauseam. 

Am I right that the type of maths is limited? If so, why is it limited? Does it matter? 

I have my own views on this.

In The Money Formula David Orrell and I compare and contrast quant finance with mathematical biology. The latter should be an inspiration for quants. But sadly very, very few quants know enough mathematics to appreciate the possibilities of modelling. (I can only think of a couple who do!) 

Thoughts?
 
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Gamal
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 6:28 am

There's nothing like mathematical biology, Paul. There's some mathematics loosely inspired by the vocabulary of biology, presumably to get some financing.
 
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Paul
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 6:57 am

There's nothing like mathematical biology, Paul.
I agree, it's a fantastic subject! (I think you mean "It's nothing like...")
There's some mathematics loosely inspired by the vocabulary of biology, presumably to get some financing.
Again, not sure what you mean. Are you saying that Mathematical Biology doesn't exist? Or that there is a tiny bit of Math Biology in quant finance, but only there for marketing? Let's go with the second...

I said it should be an 'inspiration.' There is a far broader range of mathematics in biology than in finance. Their models are sometimes accurate and sometimes 'toy.' All v similar to how finance should be treated.
BTW I'm not attacking anyone's life work here. (Although that may happen later!)
Also, nothing wrong with 'marketing.' Marketing is why none of you is living in a cave. (Apologies to any troglodytes who have made this a lifestyle choice.)
 
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Gamal
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 7:22 am

 Are you saying that Mathematical Biology doesn't exist? 
Of course it doesn't. There's only some mathematics loosely inspired by the vocabulary of biology. Biologists don't understand it, don't care and are completely right.
 
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Paul
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 7:25 am

Silly boy!
 
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Gamal
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 7:43 am

Paul, so called Mathematical Biology was my subject before switching to finance, namely Kimura model for evolution. It's some time back but still remember issues, people and biologists' comments.
 
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Paul
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 8:26 am

But the same is true of any field trying to apply maths, including finance. 99% of research is not used. I don’t see that as a reason for narrowing one’s field of vision! It’s a reason for the opposite. “Hey, this research was useless last time, let’s do more of it!”
 
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Gamal
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 8:47 am

But the same is true of any field trying to apply maths, including finance. 99% of research is not used. 
In biology it's 100%. Mathematicians and biologists don't understand each other, so they don't talk and even if they are forced to talk, they don't listen to the counterparty.
Mathematics is like poetry, everyone hates poetry, everyone hates mathematics and mathematicians. In finance mathematicians are a bit useful, so they can't just so get rid of them. In biology maths is so far useless.
 
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Paul
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 12:59 pm

Clearly you’ve had a traumatic experience!
 
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Gamal
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 1:21 pm

Working with Kimura model you invite problems.
 
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Cuchulainn
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 3:52 pm

at's a Kimura model?
The only one I know is the famous + painful/traumatic Kimura lock.
Last edited by Cuchulainn on July 11th, 2018, 4:23 pm, edited 1 time in total.
"Compatibility means deliberately repeating other people's mistakes."
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http://www.datasim.nl
 
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Paul
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 3:57 pm

The Kimura model looks like a transition probability matrix thingy??? No wonder you were traumatised! So you moved into a subject with more such matrices? A sucker for punishment!
 
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Cuchulainn
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 4:21 pm

It's  exp(Matrix) and d/dt exp(M) etc? PW has a section in his book on transiton/inteinsity and universal Markov Chains 40.13.

But DNA analogies are probably not the same as predator-prey models? Look at the successes of GA and DE.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl
 
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Paul
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Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 4:45 pm

So both math biology and math finance are a mess. Is that right?
 
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neauveq

Re: Is the type of mathematics found in finance limited?

July 11th, 2018, 6:23 pm

The question I have is this: Having only possess a very limited background in maths, should I then strive to learn the 'limited' maths of finance well (which is no easy feat in itself) or should one learn as much maths as one can outside of the 'limited' scope of finance and continuously think of applications to existing problems in finance? I am struggling to see the trade-off here. Will more maths outside of the 'limited' scope be helpful? Will more time spent on 'other' maths help me understand the current maths of finance better? I guess I am still very early in my maths journey. I am sure for other mathematicians out there the answer seems clear and self-obvious.