Welcome J1 to your new academic life :)

We at The Culture have been receiving calls recently since the start of the J1 orientation program about our tuition program. This post is a shoutout to those students who are interested in the [...]

Geometric Brownian Motion

This is really important for anyone interested in Finance Modelling. As what the movie Wolf on Wall Street says: They are referring to a geometric brownian motion. Firstly, we will begin with the [...]

Complex Number Problem #2

Show that . Hence show that For the first part, we can simply apply Euler’s Formula, that is The next part is a little more tricky, and since its hence, we will use what we solved [...]

Introduction to Brownian Motion

Lets look at brownian motion now. And yes, its the same as what our high school teachers taught about the particles moving in random motion. Here, we attempt to give it a proper structure and [...]

Review of Basic Probability

So I understand that I lost many readers for the Sampling uploads.It is a bit difficult to the intensive use of notations and also the need for statistics knowledge. So here I’ll review a [...]

Introduction to Martingales

This is a rather important topics for anyone interested in doing Finance. Lets look at their definition first. A Martingale is a random process with respect to the information filtration and the [...]

Multivariate Distributions

Let be an n-dimensional vector of random variables. For all , the joint cumulative distribution function of X satisfies Clearly it is straightforward to generalise the previous definition to join [...]

Some things that JC students should know.

In all these years of teaching, I realised that many JC students still do not know a handful of things. So I will list down a few random ones that I can recall off-hand, and of course expand a [...]

Conditional Expectations and Variances

Here we look at an important concept that is an extension from Bayes Theorem, which we discussed briefly. The condition expectation identity says The condition variance identity says Here both [...]

Continuous Random Variables

We look at the definitions first. A continuous random variable, X, has a probability density function (PDF), if and for all events A The CDF and PDF are related by It is good to know that we have [...]

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