# Mathematics

Stochastic Differential Equations are equations with a random term in them

Partial Differential Equations are equations that have more than one independent variable

Ordinary Differential Equations are equations that have only one independent variable

${\left(a+b\right)}^{2}$

Generally the longer the time that the money is tied up, the higher the rate of interest, although this is not always the case.

The offsetting of risk by buying other related contracts is called hedging

All the prices are determined by the laws of supply and demand. If there are more sellers than buyers the price will go down. If there are more buyers than sellers then the price will go up

Buyers are referred to as having long positions; sellers are referred to as having short positions

One advantage that makes Equities attractive is the potential for making very large gains

One disadvantage of owning equities is that shareholders are last to be paid if the company gets itself into trouble

If a company did not generate enough cash flow to service all its debts, preference share holders are paid before normal shareholders

Investors buy preference shares because they offer a "higher" steady income

The larger the underlying share price the larger the changes

Every company has a maximum number of shares that it can create. This is referred to as the number of shares that are "authorised"

Investors that borrow money to buy stock may be asked to make a "margin call" (i.e. to deposit additional collateral) if the value of the stock drops substantially

Shorting a stock is considered to be riskier than buying a stock. Since there is no limit on how high the value of the stock can go.

A monopoly is a situation where only one company exists or is a dominant position in that market.

A cartel is a situation where all the companies in that market agree to charge the same prices instead of competing against each other.

The liquidity is the measurement of how easy it is to buy and sell the shares.

Almost all returns are expressed gross (before tax) to allow for easy comparison.

Heath-Jarrow Morton Framework

Stochastic Processes

Black Scholes Option Pricing Model

Brownian Motion - a random process that is normally distributed with a mean of zero

Concavity of the log function

Book

Mathematics of Derivative Securities - Cambridge Uni Press

Monte Carlo Simulation is a method of random sampling, and non recombining trees are representations of how a value evolves in which branches don't connect at future nodes.

Fubinis theorem - indicates when the order of integrals can be changed to derive the main result.

khanacademy.org

### Algebra

Algebra is the language of calculus

You cannot do calculus without algebra

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