# General maths financial maths

He is active in promoting the sensible use of mathematics in finance and highlighting the need for more research into mathematics in order to better understand random and complex environments.

This shall always be clarified in the question and in fact most HSC 2 Unit Maths questions will clearly state it. Of course, financial institutions do not keep track of these fractions of cents, and interest payments are rounded to the nearest cent.

Prior to becoming an academic, he worked for sixteen years in the oil exploration industry. This is because during the last three quarters of the year, the depositor is earning interest on the interest previously earned.

Since Cardano, financial maths has been about understanding how humans make decisions in the face of uncertainty and then establishing how to make good decisions. A no-arbitrage price is not simply an expectation using a special probability; it is only an arbitrage-free if it is risk neutral and will not result in the possibility of making or losing money.

A recent example from the HSC 2 Unit Maths exam was this: First of all we have to understand if this is a "loan" or "investment" question.

### General maths financial maths

What is the principal loan amount? However, some harder versions of 2 Unit, or even Extension 1 questions that may get this as "Harder Application of 2 Unit" state that the contribution is made at the end of the period. Examples are loans, deposits, and annuities. This type awards more marks than usual and should look something like this: The first part of the question is a regular annuity question, so we have to derive the balance formula as above and substitute the values given. He introduced the law of large numbers, proving that if you repeat the same experiment say rolling a dice a large number of times, then the observed mean the average of the scores you have rolled will converge to the expected mean. Since no formula is given for the net balance at Jules's retirement, we need to first derive it as discussed above. However, as with much of probability, what seems simple can be very subtle. We can solve these questions in pretty much the same way as the investment examples above, with one major difference: all contributions will have 1 less period to be compounded. If you stop and think about this premise you should quickly realise it has little to do with the practicalities of business, where the objective is to make money without the risk of losing it, which is called an arbitrage, and financial institutions invest millions in technology that helps them identify arbitrage opportunities. Drawing from an initial balance until it gets to 0, is the same situation as a loan - so you should treat these questions exactly like the loan example above.

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