It has been a while since I wrote an article. I therefore owe you, my readers, a sincere apology. With the ever looming lockdown coming for Kuwait in February 2021, I decided to take a deep breath from university studying — to pause, reflect, and continue writing once again.

An interesting subject I’ve recently came across was ‘Game Theory’, and therefore I’ve selected it as the first article to once again revive the streak of article writing in 2021. …


Disclaimer: This article series recommends the use of Matlab. If you do not have access to Matlab, then try using Octave which is an open source alternative with almost completely similar syntax. You may use this online version https://octave-online.net.

Contents

1- Mathematical Models and Computers

2- Matlab Basics

1- Mathematical Models and Computers

Look at the world around you. You can make sense of many aspects of it. Take it a little further, you can predict a fairly good amount of it. For instance, grey clouds cover the sky — you automatically make the prediction that it will rain. That is an example of a very…


In this particular article, I’ve decided to try out a slightly different style of relaying information. The basic philosophy is as follows: I’ll provide low resolution information on a particular topic, then as we go through the article it will gradually be recalled again to where a higher resolution of it is provided. Fingers crossed it works as intended (Please let me know in the responses if it has).

Contents

Part 1: Investment Instruments

Part 2: Portfolio Theory

Part 3: Portfolio Optimization

Part 4: Application of Portfolio Optimization

Conclusion

1- Investment Instruments

It is not uncommon to be bombarded left, right, and center by…


What is the opposite of fragile? Robust? Wrong!

It’s natural. Most people would often say robust — something that is not fragile, something that does not break. Whilst this common answer may seem correct at first, one can view fragility in a totally different light.

To understand the question better, let us first ask:

What is fragility?

Fragility is used to describe something that easily breaks or is damaged by a stressor/disorder; this means it is a negative response to a stressor.

Meanwhile if something is robust, then it is strong and durable when a stressor/disorder is applied — meaning it is a…


From observations to drawing up strategies.

In light of the recent relaxation of the curfew in Kuwait and hence the reappearance of traffic, an idea I had previously thought, has once again resurfaced.

Every morning as I traversed my usual route to university, which consists of traveling on the Arabian Gulf road, rerouting to get on the 4th ring road, and then it was a continuous straight road to my destination. …


Contents

Part 1: What is Pairs Trading?

Part 2: An Overview of Pairs Trading

Part 3: Conclusion

1- What is Pairs Trading

As a primer to our current topic, I would strongly suggest reading another article I wrote on the concept of arbitrage.

With that said, I can formally introduce the definition of arbitrage as such:

An arbitrage (portfolio) is one where you pay nothing to enter it, and you make a certain risk-less positive profit.

There are a few instances in the market where arbitrage opportunities occur. The one we will consider will be an inter-stock instance. …


Contents

Part 1: A Primer on Classical Logic

Part 2: The Real World

Part 3: An Introduction to Fuzzy Logic

Part 4: Modeling Trading Decisions

Conclusion

1- A Primer on Classical Logic

Thanks to the Abbasid empires goal of translation and preservation of Aristotles texts, we maintain the robust two thousand years old Aristotelian logic known to us today as: Categorical Logic. Essentially, it forms the rubric of classical or traditional logic.

Over the years categorical logic gave birth to formal logic — which sees heavy usage in discrete mathematics. You can brush through discrete mathematics concepts and the topic of logic in this article:

There are…


Primer

In a previous article, we utilized a very important assumption before we began using the concept of a random walk (which is an example of a Markov chain) to predict stock price movements;

The assumption here of course, is that the movement in a stocks price is random.

Be sure to check out this article to see how we used coin tosses to predict stock price movements by using a geometric random walk to yield surprising results.

Here we will carry on with that assumption which allows us to call upon the use of ideas from probability — namely we…


The Mathematics of a Coin Toss

A coin is a very interesting item. This is because its intriguing aspect truly lies with its use in probability, rather than it’s function as a monetary item.

Coins are widely used as a tool to aid in randomly selecting between two choices. What makes a coin perfect for this job is the fact that it has two sides: Heads (H) and Tails (T). The act of tossing a coin is indeed a random experiment. There are realistically only two possible outcomes (binomial probability), either heads or tails. …


What is chaos?

It is a seemingly random behavior exhibited in a system, with sensitive dependence on initial conditions. What we mean by ‘seemingly random’, is that this behavior is very unpredictable — so much so that it may appear random. This random appearance is due to the fact that the changes in behavior are extremely sensitive to the initial conditions of the dynamical system. In essence, chaos is the study of small changes that significantly change the future of a system.

What is a Dynamical System?

It is a system that can be described with a function with time dependence of a…

Abdulaziz Al Ghannami

An aspiring quant & writer at : www.ghannami.com

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