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Today, 12:50 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends, today I was thinking of some other possible and general way to find a good guess for Newton method in the context for moment/cumulant calibration. I think I have some new workable ideas. I am trying to work with a new method which is a combination of Taylor series and matrix manipulations i...
Yesterday, 8:41 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends, I have mentioned several times that I want to start algorithmic trading in vanilla stocks. Several months have passed since I opened a trading account with Interactive Brokers. But unfortunately I could not fund my account due to foreign exchange restrictions in Pakistan. IB would not accep...
August 8th, 2022, 4:46 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

As a start, friends can try running the program with input cumulants as given in the above graphs in previous post. , , , function [b0,b] = FindZSeriesGivenCumulantsStandard07() mu=0; sigma=1.0;  k1=0.0;  k2=(1.0);  k3=0;%1.0;  k4=2.5;%-.50;  k5=0.0;%-.5;%15;  k6=150;%10;%100.0;  k7=0; % k8=1400; [m...
August 8th, 2022, 3:16 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends, I have tried plotting some graphs of densities with fitted cumulants and target standard cumulants along with the Z-series coefficients on the title. Not every combination of cumulants is possible. Here are the graphs. The blue density is that of standard normal. . . . https://i.postimg.cc/...
August 8th, 2022, 10:48 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends I have been able to extend earlier six cumulant, up to fifth power Z-series representation to seven cumulants or sixth power Z-series. But I have not been able to add the eighth cumulant in calibration in a stable way. I will post the seven cumulant program with graphs later today but will h...
August 4th, 2022, 12:55 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends, I am writing this post about gas in the Air-conditioners. It is summers and monsoon rainy season and it becomes hot and humid on many days. I had been trying to work in the drawing-room of our house where I would turn on the AC and then try to work. It worked well only for first few days an...
August 3rd, 2022, 10:20 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends I spent some time yesterday, rather unsuccessfully, trying to see if there could be some very simple way of extending the six moment Z-series representation to higher order in moments and coefficients of Z-series but very simple ideas did not seem to work. I still have not tried ideas I had ...
July 30th, 2022, 12:01 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends, In the previous post I said that they were not using any gas on me while I would sleep. I was just trying to sleep to have a nap for an hour and a half but they started to use gas in my room. Probably they were emboldened because I had just mentioned that they were not doing anything like t...
July 30th, 2022, 8:05 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends, sorry that I have not posted for the past whole week. I have an extreme urgency to be able to make some money. Some money I receive from my parents has been the same for past ten years but prices of everything have increased by 5-6 times and it is almost impossible to survive. So I started ...
July 26th, 2022, 10:29 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

I want to write this post especially to thank friends who made it possible for me to work on my research by protesting to mind control agencies about my persecution. Several years ago when I was largely on my own, it was extremely difficult for me to consistently work on my research. At that time, t...
July 26th, 2022, 8:50 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends, here is the general program which takes input raw moments and calculates  its Z-series and also draws its graph. I have provided a small routine that takes a general mean and a general variance and standardized cumulants to create valid raw moments. If your density is surely valid, you can ...
July 25th, 2022, 12:37 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends, I will post my general program tomorrow. But briefly I want to mention that standardization used for central moments is exactly the same as standardization used for Z-series coefficients (we have to do some very simple accounting for mean). So once we specify a general density and calculate...
July 25th, 2022, 8:42 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Later tomorrow, I will post a simple program that will show how to take arbitrary moments (that are meaningful and coherent) , standardize them, find Z-series of standardized density and then convert Z-series of Standardized density to Z-series of original density with initially specified arbitrary ...
July 25th, 2022, 7:48 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

You can also find Z-series for densities with fourth cumulant smaller than zero. But as I mentioned in previous post, you have to specify some positive value for sixth cumulant. You can specify some small skew with negative fourth cumulant. Here are graphs of a few such densities . . https://i.posti...
July 25th, 2022, 7:36 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1514
Views: 213804

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

With standardized moments, i.e k1=0, and k2=1, you can only specify upto k3=+/-.4, if k4=0, k5=0, k6=0. Similarly you can only specify k4=+1.5 when other cumulants are zero. You can increase k4 to 4 or 5 but for that you would have to judiciously increase k6. Similarly you can increase k3 to +/-2 bu...