Back to Warwick
First of all, sorry it’s been a while; I’ve had a very busy few months!
This term has been great so far, in fact I would say the best term of university so far. My modules this year have been incredibly interesting. This term my favourite module has been Mathematics of Random Events. We have been learning about a mathematical object called a measure. Now it’s a different way of looking at integration, that I’m sure you’ve encountered already, though it’s very applicable to probability which is where I guess I will use it most. So what does a measure mean?
We need a measure to integrate the empty set (nothing) to 0, the integral has to map between 0 and infinity. Finally it is has to be sigma-additive which means you have to be able to sum disjoint measures. What’s really interesting is how different measures can give such different values. I wish that I could have been shown this earlier, it’s like a whole new set of maths and it’s hard to adapt the knowledge I already have into it.
My other modules have been mainly finance based: Introduction to Mathematical Finance and Actuarial Methods. Actuarial Methods leads to an exemption from CT1 which is an actuarial exam that you would have to take to become an actuary. We have been looking at usual financial objects such as annuities, perpetuities and pricing bonds. Something I really recommend looking at.
Mathematical Finance has been dealing with choosing portfolios of assets and bonds. This has gone into utility functions which is measuring people’s utility (happiness) based on wealth etc. We normally assume these functions are concave naturally. Now we are dealing with arbitrage which is when there’s profit to be made in the market with no work to do. So simply buying something and selling that thing for an instant profit (could be any time period).
My final module is Bayesian Statistics and Decision Theory. Analysing how people make decisions and ensuring it’s the right decision. More recently we’ve been looking at whether two different random variables (a measure from before!) are dependent on each other. I am thinking about doing an advanced version of this module which will mean I can do an easier module next year and not a master’s module.