Optimized Risk vs Reward Equation

OK, after a dozen pages or so, here's something that everyone should understand, a really easy way to do constrained optimization in excel and get reports with lagrangians.

First video, about excel solver and one easy example:
http://www.youtube.com/watch?v=uQU1KfsE5us

Second video, with just a little bit more complicated function:
http://www.youtube.com/watch?v=m1_P27gbNhk

I've also made a small table, using the data from second video.
What is left to do? Trial and error with different functions with saddle points and different constraints. Each solution will represent entry data for the next transaction. You don't have to do any hard math, solver will do it for you. :nerd:

bigvlada,

Do you have a rice cooker? Mine has inspired me to start applying Neuro-fuzzy logic to my FX..

Rice and water are not a linear relationship; most people don't know that. The more rice, the less water you need. So a neuro-fuzzy logic system has to be implemented to cook perfect rice every time. While FX prices go up and down, I don't think the relationship is linear either; so I've taken some methods from my rice cooker and applied it to FX.

Since you seem to like research everything I'm researching, there you go.

Some unless facts and history:
The first neuro-fuzzy logic algorithm to be applied to a rice cooker was done by a good friend of mine named, Felix; who was a Russian space program, programmer who got laid off and picked up by a Japanese company to program rice cookers.

http://home.howstuffworks.com/rice-cooker2.htm

Enjoy!

No, no rice cookers, French fries makers, pastry makers and especially, no microwave ovens for me. I really like to cook and am a firm believer that microwave is the antithesis of good cuisine. Only open flame, oven and sometimes pressure cooker (in order to save time). Even when I want to eat pizza, I make it, including the dough (it's less than 60 minutes job in total).



Hmm, I thought they were. But above mentioned sentence must have certain limitations, boundaries - you can't cook 10 kilograms of rice in 6 dl of water.

If you set the volume of water as an constant, and adding small amount of rice, it will cook faster, but it will be bloated and prone to decomposing. Too much rice and it will be hard and uncooked.

Problem is, there are more variables in this problem - time and species of rice (in the Balkans, the most sought after is Macedonian rice, but Indian and Chinese is present as well). Different rice will need different amount of water and time in order to be cooked well.

But i understand the analogy:

IF temperature IS very cold THEN add much more power
IF temperature IS cold THEN add more power
IF temperature IS normal THEN maintain level
IF temperature IS hot THEN subtract power

Can these cookers adjust the amount of water accordingly?
Now when I think about it, washing machine is the ideal piece of household appliance to be based on fuzzy logic.

What we are trying to do here is the same:

We know there is an equilibrium, represented as saddle point. Looking like that, the hmmm, transaction regulator, perhaps an EA, paired with an excel table would base his decisions on something like this:

IF the price is reached THEN enter transaction
IF the sl is reached THEN close transaction
IF the first tp (saddle point) is reached THEN add another transaction (in accordance to excel table)

The EA should adjust lot size in order to fulfill initial parameters of lot size, stop loss size and risk.

Here's a picture of basics of fuzzy analysis. In it, there is also a need to find the smallest value of one variable and largest of other which satisfy some function.

Fuzzy logic non linear constrained optimization - I mustn't tell this expression to anyone I know or I'll end up in a loony bin.

Most rice cookers can only control temp, but mine controls temp and pressure.. It has a rice selector so you can kind of give it a hint on how to cook the rice.

It has an internal and external thermostat though; on a hot day, it will actually reduce heat to make sure temp rise doesn't go crazy.. It's fairly smart and perfect rice almost every time (within reason). If it senses that you have too much water in there (I assume steam to temp analysis ratio) then it will lower the pressure to compensate; and if visa versa; it will raise the pressure to compensate. A lot of technology goes into perfect rice.

The Microwave is a great tool; I use it to warm my plates.. It wasn't designed to actually cook food.. I use it for the 2 things it was meant to do: heat plates; and dis-infect sponges.. 2 minutes on high!

I figure you needed to complicate your life a bit more.. so there you go..

Fuzzy logic non linear constrained optimization ~ FX is closer to rice than you think! If someone asked what you've been working on, and this was your answer, they'll think you are smart..or crazy..

Fuzzy logic and probability are different ways of expressing uncertainty. While both fuzzy logic and probability theory can be used to represent subjective belief, fuzzy set theory uses the concept of fuzzy set membership (i.e., how much a variable is in a set), probability theory uses the concept of subjective probability (i.e., how probable do I think that a variable is in a set)

Suppose we are given a mathematical programming problem in which the functional relationship between the decision variables and the objective function is not completely known. Our knowledge-base consists of a block of fuzzy if-then rules, where the previous part of the rules contains some linguistic values of the decision variables, and the consequence part is a linear combination of the crisp values of the decision variables. We suggest the use of Takagi and Sugeno fuzzy reasoning method to determine the crisp functional relationship between the objective function and the decision variables, and solve the resulting (usually nonlinear) programming problem to find a fair optimal solution to the original fuzzy problem.

The above paragraph is from Optimization under fuzzy rule constraints paper.

hmm, using fuzzy control language to articulate the problem would mean that even the optimal value function's expression would depend on the value of the constraints. If one of the constraints is small the f(x) could be x+1 and if it is big it could be 2x+5. With two constraints, the situation gets even more complicated, because there are even more possibilities. For each of these possibilities, we have to find optimal non linear constrained solution. The problem is, How do we know when some constraint should be labeled big or small?

This morning, I figured out the answer to the "high/low" paradox; which has plagued me for almost 4 years.

I read a bunch of books in the last 2 months about how to be a bookie; not so much that I wanted to be one, but the "bookie dilemma" that plagued me as well.. and I really wanted to solve it.. I have..

So I'm excited.

If someone is actually interested in the 2 problems; I'll explain them, otherwise I won't bother with the somewhat mundane overview of the problems.

Im all ears:nerd:

I'm not sure I can explain the high/low situation without complex graphs..

Just did a full pdf writeup on both of these things tonight actually..

so will give you the bookie dilemma:


Problem: The Bookie's Dilemma

Description of the Problem: This isn't so much a problem for the bookie as it is for the person making a bet with the bookie.

So let's say Lakers vs Celtics are playing. You call up your bookie and he says, if you bet $100 on the Lakers and the Lakers win, you will be paid $190. If you bet on the Celtics, who have slightly worse odds; if you bet $100, then you will be paid $191.

100:90 Lakers
100:91 Celtics

So if you are the bookie; you make your money because you make 10% against the Lakers, and 9% against the Celtics. So if 50 people bet on the Lakers, and 50 people bet on the Celtics, then you'd rake an average of 9.5% regardless of who won. But that's not where the money comes from; if there is less than 10% of a difference between the bets for either team, then not only would you come out ahead; but you'd make “juice” (interest) on the money that was owed to you; and juice is usually high like 15% a week or so.

So there in lies the bookie's dilemma. If you are the better, how do you win; long term? You either gotta be so good at picking which team will win; or else you will have to understand how to defeat the system they've set up.

If the chances of Lakers vs Celtics is a baseline 50/50, then the less deviation from it; the more long term wise the bookie is going to make. If you substitute “bookie” for market maker; then you have defined the bookie's dilemma. How do you defeat an FX market maker? They have a bid/ask spread PLUS if you are on the wrong side, you will be paying interest on your money.

So that's the bookie dilemma. Read quite a few books to solve this one..

I'm going to read the whole thread. this looks like one of the good ones.

I will try to without diagrams, explain the high/low paradox..

So let's say you are long on a position; and you want to add to that position. You would normally add if proven correct (a la Phantom's Gift) and so if you are long, that means you would buy when a higher high is broken and a new high established. (The high side of the paradox)

But if you put an SL, you will more than likely put it at a low of some bar.. (the low portion)

So assuming a long position; we always BUY on the HIGH marks of a bar, but SL on the LOW's of bars.. and so you can enter once, or multiple times, and still lose your shirt because highs get broken for an entry indication but lows get broken for an SL. The gap (high - low) is your risk; and so you ALWAYS intrinsically greater risk simply because you know your entry point is based on the extreme side (high) but your SL is based on the extreme side (low).

But the paradox comes in that, you can't actually logically go long against a bar low; nor can you logically SL against a bar high if you are on the long side.. and of course visa versa for the short side.

But you don't know what your up side target is?

Today, I also solved the "Average Up / Average Down" Paradox; and this also leads to solving the "I pick up, you pick down" paradox.

So the problem is:

If I have a position and I'm wrong, and I buy another position, I therefore am averaging down; which is martingale which will bankrupt me.

But, if I'm correct and buy another position; I cannot average up and break the 1.00 expectancy barrier as each additional position lowers my probability.

So the paradox is this: how can you lose money averaging down, and then STILL lose money when instead, you averaged up?

This is related to the other problem...

If we started trading, and every time a trade decision is made; you would pick the opposite trading situation from me (so if I bought, you'd sell, if I sold, you'd buy) so we'd hold exactly opposite positions from each other.. More than likely, upon exiting our positions, BOTH of use would lose money. That is what I call the "I pick up, you pick down" paradox.

If I am dealing with an expectancy of 0.95, in theory, if you took every opposite position from me, shouldn't you have an expectancy of 1.05? Nope, that is not the case. Both will more than likely lose, and neither will have a > 1 expectancy.



I've been at this for about 4 years now; and I actually think, I've solved every single math/logic problem involved in FX that I've set out to solve.

I've even solved the SL problem today.

So good day all around. Always thought that I would be able to solve all these math problems; but in the back of my mind; I had a nagging feeling that if these were solvable, why hasn't anybody solved them yet? The Conspiracy Factualist in me though thinks that these might have been solved already by people who are part of a secret society who meet once a year in Liechtenstein.

Zurich actually. We meet in Zurich.

Zurich? You must be in the wrong group! hahaa..

In all seriousness; testing out my new found math.. and it's doing quite well...

My intuitive take on this is that we have to assume how prices are distributed. Given a distribution we have a characteristic function. Then we can use a cumulative distribution function and a probability density function to represent probabilities of outcome.

I deal with something I call "Propensity". I use it instead of saying a statistical advantage because I usually can't prove the math of it; OR; the statistical advantage is there but might not be, depending on how much you are paying for bid/ask.

One of the biggies though was figuring out that:

As N -> Infinity; Expectancy via averaging down (Martingale) asymptotically approaches 0.

I knew that already.. What I didn't know until recently was:

As N -> Infinity; Expectancy via averaging up (Anti-Martingale) asymptotically approaches 1. It doesn't reach one, it approaches one..

With that piece of knowledge; I was able to come up with another system to break the 1 barrier.. Whats even better is I wrote out a math proof that it indeed breaks the 1 barrier...

You have actually proven this? With any price series (or in other words what price distribution did you use when you proved this)?

Yes. I've got 60+ gigs of data to backtest against. All major pairs from 2007 to today.

Could you shed some more light on the research you did?

Which part; and how much light?