I am currently evaluating everything, I will update you very soon.

Statistics: Posted by SamHarper — Today, 6:12 am

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Cuchulainn wrote:

Yes -- more specifically, I refer to the attached article:

Lewis.SimpleAlgorithmPortfolioSelection.pdf

I think this is a great place to start. I am travelling for the next few days across the wide open sea(s) and I hopefully will have internet again soon.

Statistics: Posted by Cuchulainn — Yesterday, 11:41 am

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Will 100% release end product, either on here or Cuch can send.

I'm hoping we can produce something very special, as a number of key individuals have offered to help in a few crucial ways!

Thanks once again, you have been so helpful.

Statistics: Posted by SamHarper — July 16th, 2018, 10:03 am

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I thank Alan and ppauper for their input.

Statistics: Posted by Cuchulainn — July 16th, 2018, 9:10 am

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Yes -- more specifically, I refer to the attached article:

Statistics: Posted by Alan — July 15th, 2018, 7:35 pm

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http://www.johnboccio.com/MathematicaTu ... zation.pdf

Statistics: Posted by Cuchulainn — July 15th, 2018, 6:47 pm

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Alan wrote:My guess is this is either a homework problem or a problem given to a summer intern. It's so vague that I'm inclined to go with the latter. Either way, the problem goes nowhere until you (or the problem's author) specifies an objective function.

Some things to think about. (Let's assume the objective function is the expected trading profit).

-If the stock price is expected to go up, why not just liquidate as slowly as possible (given the constraints)?

-If the stock price is expected to remain unchanged or go down, why not just liquidate as rapidly as possible?

In other words, very often solutions to dynamic programming problems are trivial!

Hi Alan,

Thanks for your help. It is in fact for a masters thesis. And again you are right, my objective function is, as you say, Expected Trading Profit (ETP).

Looking over what you've said is right, even in the scenario where it doesn't rise/fall continuously, I can rank the predicted prices and then use a simple allocation that still adhered to the constraints. So thank you for making me realise there does exist a simple solution (as usual)!

However, in my opinion, my problem is that the future price predictions might not be specifically true, so how to hedge this risk? For example, let's say I use minimum trading limits every day until the last 3 days as I believe the price will rise. Then suddenly, the prices actually dive and I am left with the maximum daily trading limits with the price being low. Therefore I would have to liquidate all remaining assets over these 3 days at an extremely undesirable price.

How could I still try to maximise my reward (ETP) while accounting for the risk (predictions aren't 100% accurate)?

Thanks for your response.

Kind Regards

Sam Harper

You're welcome.

@SH and Daniel,

The objective function is up to you. A more general one that accounts for risk is

[$]\max E[U(W(T))][$].

Here [$]W(T)[$] is your terminal wealth, [$]U(W)[$] is your utility function, and [$]E[\cdots][$] is an expectation. Utility functions are subjective: there is no universal prescription. However, certain utility functions can simplify the resulting optimization problem. For example, [$]U(W) = \log W[$] accounts for (some) risk, can result in simplified "myopic" decision making, and is well-studied under the name "Kelly criterion".

Mathematically, the resulting portfolio selection problem (perhaps your problem is simply portfolio selection with the constraint of being 100% in cash by time T), can be solved by iterative quadratic programming. I wrote an article on that long ago. However, again, your constraints may be saturated and the solutions trivial, esp. if you don't have any special knowledge about what is going to happen to the stocks.

Statistics: Posted by Alan — July 15th, 2018, 2:50 pm

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One relevant aspect is whether the problem (which must still be defined) has already been addressed and what your added value is.

A good tip is to implement a software proof of concept/prototype based on Alan's and ppauper's ideas, for example.

edit:

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Alan, ppauper

For this problem don't we want to maximise expected value _and_ minimise the standard deviation?

Statistics: Posted by Cuchulainn — July 15th, 2018, 11:44 am

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ppauper wrote:Alan wrote:Some things to think about. (Let's assume the objective function is the expected trading profit).

-If the stock price is expected to go up, why not just liquidate as slowly as possible (given the constraints)?

-If the stock price is expected to remain unchanged or go down, why not just liquidate as rapidly as possible?

according to the pdf, he's allowed to go short. If the stock price is expected to go down, if the constraints allowed, I would not only sell what I owned, I'd short the stock as well.

And if the price is expected to go up, I'd buy more.

You'd want to hold a portfolio on the efficient frontier

Hi ppauper,

Thanks for your response!

However, my question is, would you still buy more if the objective of the task was to liquidate the portfolio by time T? Surely it would actually be working against the constraints?

Sam

it depend on your constraints.

If you're charged to (a) liquidate the portfolio by time T and (b) maximize the proceeds, then yes, I would sell the "worse" stocks and put the proceeds into the "better" stocks, and then sell before time T

Statistics: Posted by ppauper — July 15th, 2018, 11:37 am

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-If the stock price is expected to remain unchanged or go down, why not just liquidate as rapidly as possible?

Sam,

How easy is it to design these two cases for a single stock?

Can you paraphrase the algorithm(input, output, steps) in English that a layman (almost) can understand it?

Hi Cuchulainn,

Great idea, I will write it in layman terms. Once again, going back to basics is the best way!

Hope you're well

S

Statistics: Posted by SamHarper — July 15th, 2018, 11:19 am

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Alan wrote:Some things to think about. (Let's assume the objective function is the expected trading profit).

-If the stock price is expected to go up, why not just liquidate as slowly as possible (given the constraints)?

-If the stock price is expected to remain unchanged or go down, why not just liquidate as rapidly as possible?

according to the pdf, he's allowed to go short. If the stock price is expected to go down, if the constraints allowed, I would not only sell what I owned, I'd short the stock as well.

And if the price is expected to go up, I'd buy more.

You'd want to hold a portfolio on the efficient frontier

Hi ppauper,

Thanks for your response!

However, my question is, would you still buy more if the objective of the task was to liquidate the portfolio by time T? Surely it would actually be working against the constraints?

Sam

Statistics: Posted by SamHarper — July 15th, 2018, 11:18 am

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My guess is this is either a homework problem or a problem given to a summer intern. It's so vague that I'm inclined to go with the latter. Either way, the problem goes nowhere until you (or the problem's author) specifies an objective function.

Some things to think about. (Let's assume the objective function is the expected trading profit).

-If the stock price is expected to go up, why not just liquidate as slowly as possible (given the constraints)?

-If the stock price is expected to remain unchanged or go down, why not just liquidate as rapidly as possible?

In other words, very often solutions to dynamic programming problems are trivial!

Hi Alan,

Thanks for your help. It is in fact for a masters thesis. And again you are right, my objective function is, as you say, Expected Trading Profit (ETP).

Looking over what you've said is right, even in the scenario where it doesn't rise/fall continuously, I can rank the predicted prices and then use a simple allocation that still adhered to the constraints. So thank you for making me realise there does exist a simple solution (as usual)!

However, in my opinion, my problem is that the future price predictions might not be specifically true, so how to hedge this risk? For example, let's say I use minimum trading limits every day until the last 3 days as I believe the price will rise. Then suddenly, the prices actually dive and I am left with the maximum daily trading limits with the price being low. Therefore I would have to liquidate all remaining assets over these 3 days at an extremely undesirable price.

How could I still try to maximise my reward (ETP) while accounting for the risk (predictions aren't 100% accurate)?

Thanks for your response.

Kind Regards

Sam Harper

Statistics: Posted by SamHarper — July 15th, 2018, 11:15 am

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