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# A strategy question

Wed 13 Sep, 2017 02:18 am
Hello everyone.

I have a problem need to be solved, I do not know which catalog this question belongs to. But let me give an example to demonstrate this:

Let’s say there is a stock. When the price is 100, I bought it, I am certain the price will go up, and at some point, I am not that certain anymore, let this point be price at 150. Apparently I have 50% profit at this point. Now, I sensed that, the price might goes down, but eventually it has a probability that go up again like up to 300. About the highest price 300, I do not know the exactly number, but when it goes there, I will know it is the point I sell it. So, here is the interesting thing: when the price goes down, it might go to 140, 130, 120, 110, 100, 90, even 80, I do not know how it goes, but I know, if it goes down to 80, it probably will not go back to 100 again and keep on dropping, thus, I will lose money there of course. One more restrict, once I sell this stock at some point, I can not buy it back. And, at any point higher than 80, the price could go up.

Therefore, if we hold this stock, we might lose money or get the highest profit, if we sell it at some point, it might goes up at that point then we can not make more money or it keeps dropping so we kept what we have at this point.

My question is, purely in Math, what kind of strategy we could use to get more money, and why?

If there is a related book or essay you know, could you tell me please?

Thanks!
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maxdancona

2
Wed 13 Sep, 2017 05:34 am
@hy2017,

If I understand correctly, there is a 100% chance that the stock will go from 100 to 150. So buying the stock at 100, and selling at 150 is a pretty clear good move, and you should buy as much as possible.

I need to know the probability that it will go to 300.

And I need to know your acceptance of risk (is losing \$150 dollars acceptable if you have a reasonable chance to get \$300).

I play poker, and we make this type of calculation all the time. The term in poker is "expected value" which means that if you get to make this bet a million times, what will be the average amount of profit/loss. If you are willing to risk losing all of your money (for the chance of a big profit), then the way I would approach this problem is to calculate the expected value for each strategy and pick the highest.

But there are times when the expected value isn't the important number (like when you don't want to have any risk of losing all of your money).
hy2017

1
Wed 13 Sep, 2017 10:44 pm
@maxdancona,

Yes, you are right, from 100 to 150, I could always sell it like this each time. But I do not know this is the best strategy.

Usually, I could see from 100, there is a top, like 300(potential highest value), but it could be 160, or 500, even 1000. The hard part is, I know there is a dropping(like when it reached 150 in this case), but I do not know how low it could reach, and when the price is down enough, it would prove me wrong, that there would not be a higher price, in this case, if it goes lower than 80, then the 150 will be the top value I could get, and if I still hold this stock, the price could go much lower than 80.

And I forget to say one thing, I could not afford to lose all of my money even once. Because when I have 100 dollars, I buy 1 stock, when I have 10000 dollars, I buy 100 stocks. Of course I could do something to avoid to lose everything I have, like only put 60% of money into stocks each time, then if I keep on winning, it still gives me very good money.

So, about the probability that it will go higher than 150, as you know in poker games, it is different each time, and not like poker we could have exactly probability each time, the problem is, I do not exactly know, I think I could use another example to state the probability:
When we go skiing, we would consider rent or buy a ski board, the price of a board is 200 dollars, and rent it would be 10 dollars a time. we do not know how many times we would give up skiing(probability is unknown), but I heard that in Math, it is still possible to calculate that buy this board when you rent half price is the best strategy. (I could not find this strategy solution right now, sorry about this, I just know I read it somewhere many years ago, but I could not remember the solution process. By the way, this solution helps me a lot in life of buying or renting something)

I hope I explained what you need, thanks again!
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