Kaufmann Risk of Ruin
- Thread starter virtualmoney
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Math is not just symbol manipulation. When taking the limit as T -> oo you already assume that T can get to infinity.
T is not a free, independent variable in a gambling game. Wouldn't that be nice?
I would like that you seriously think about this. Can you spot the fallacy you employed that led to a limit equal to 1?
The limit is correct but the way you derive it is mathematically wrong. T is not like time t in physics, a quantity that is independent of the underline process (save relativistic conditions).
T is a dependent quantity and as someone already pointed out it depends on the path followed.
What sense does it make to say that the probability of ruin is 1 when you have infinite capital accumulated?
Think about that. If you lose infinite capital when you already have infinite capital you still have infinite capital left.
How much is oo-oo? Ask yourself.
Math for kids that grew up with pac-man? Possibly. This is not math you employed, it is an exercise in futility.
You told us that the probability of not getting to capital T when starting with capital C but dropping to X instead is equal to 1 when T is already infinity. (For the particular case).
Do you understand what you have told us? Math is not a game of symbols. You cannot use circular references in math. Have you ever programmed anything? any code at all? Have you ever gotten a debugger response:
"circular reference encountered".
Let's get serious. Math is not pac-man.
I don't understand the math but I'll make a few statements from experience:
1. For every trade Profit targets are good to have
2. If average profits equals 2x average loss, in the long run you'll do ok
3. Dollar cost averaging helps to minimize losing trades, but do it often enough and you'll be out of business
4. Understanding esoteric maths may help improve ones market acumen, so does having the ability to program code.
5. Knowing too much esoteric math may lead to belief in fallacies such as "annualized returns" that are detrimental to a traders mental game
6. The markets are 99 parts random insanity and 1 part logical behavior. Elitetrader is a great forum to kill time while waiting for the correct 1% market signal.
1. For every trade Profit targets are good to have
2. If average profits equals 2x average loss, in the long run you'll do ok
3. Dollar cost averaging helps to minimize losing trades, but do it often enough and you'll be out of business
4. Understanding esoteric maths may help improve ones market acumen, so does having the ability to program code.
5. Knowing too much esoteric math may lead to belief in fallacies such as "annualized returns" that are detrimental to a traders mental game
6. The markets are 99 parts random insanity and 1 part logical behavior. Elitetrader is a great forum to kill time while waiting for the correct 1% market signal.
Of course it is. T is chosen by the gambler. It is in no way dependent on C, X, p or q.
Can you?
So give us the "dependent" relationship you talk about. Be specific.
You have reading comprehension problems. The risk of ruin is the probability of FAILURE. Obviously you won't reach infinite capital if the risk of ruin is one.
My mistake. I thought I was dealing with an honest broker. You are clearly one of intradaybill's sockpuppets or one of his sycophants. You also have never passed a calculus class or you wouldn't ask all these silly questions about infinite limits. Go back to school and learn something about trading math, you're clearly not ready for trading at a technical level.
Really? Do I have comprehension problems? Aren't you the one who in the process of calculating the probability of failure to reach infinite T you set T equal to infinity? So, aren't you the one who then claimed that the probability of failure to reach infinite T is 1 when T is already infinity, for q > p?
Think of it another way; can you say given a function of x which has a limit of 1 as x goes to infinity guarantees that x will be less than some number x' with probability 1? What sense does that make?
I think DontMissThe Buss was correct to call you a crank. I am asking you again crank; what sense does it make to say that the failure probability is 1 when T is infinity? This is too simple for an eight year old. Are you a grown up?
So everyone who tries to put you in order is a sockpuppet of someone else or crazy.
Bye-
Edit: as I said the calculated probability happens to be the correct number but the formulation of the program is cranky. You have to find a function for that probability where n, the number of trials, is the independent variable. Then you are allowed to set n equal to infinity at the limit to calculate the probability of failure to reach some target T, given starting C, before falling to X.
You haven't done that.
You are obviously a mentally deficient person so I will explain this s-l-o-w-l-y one last time before putting you on ignore.
There is a gambler who wants to increase his current bankroll C. He participates in an even-payoff game where he wins or loses one unit per trial. In other words, at the end of a trial, the gambler will have a new bankroll of C+1 or C-1.
He has a pre-determined target bankroll T and a pre-determined surrender bankroll X. In other words, if C grows to the level T, he wins. Game over. On the other hand, if C falls to the level X, he loses. Game over.
It should be clear that the minimum number of trials needed to succeed is T-C, which would occur with a probability of p^(T-C). Likewise, the minimum number of trials needed to fail is C-X, which would occur with a probability of q^(C-X). Obviously most games to completion would involve more trials than the minimum of T-C and C-X, and probably most would be greater than the maximum of T-C and C-X as well.
So there is no need to specify the number of trials directly. In fact it's counterproductive because we have no idea what path C will follow to get to either T or X, whichever comes first, and it's unnecessary.
You've found no fault with the general formula that I posted, yet you go to pieces when T is allowed to increase without limit.
Get help. And good riddance: jimbojim >> ignore.
He did not for sure. I agree with you on many of your points, maybe not all but the general idea you have is correct.
Basically, for q > p he proved that the failure probability of reaching a target bankroll T is 1, i.e. the certain event, if T is equal to infinity.
Who cares? This is the stupidiest statement I have ever heard in a long time. He calls that some kind of a math proof. This is because he is a crank.
The problem is to determine when the probability of failure can be 1 when the target T when T is finite. The crank still doesn't understand this.
This is a practical problem for traders and a solution can be used to filter trading systems. That does not depend just on p,q, C,T,X. It is a very complicated problem.
This is life. You start talking about a very complicated problem and some crank who does not understand the issues jumps in like a monkey pissing and jerking off all over the place with trivial statements involving infinity.