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Brownian motion is the zig-zagging motion exhibited by a small particle immersed in a liquid or gas. The Brownian motion models for financial markets suggest that financial assets have continuous price evolving continuously in time and are driven by Brownian motion processes.

Stochastic calculus operates on collection of random variables. An important application of stochastic calculus is in quantitative finance, in which asset prices are often assumed to follow stochastic differential equation.

MATHEMATICS OF INVESTMENT

1) Role of probability in investment?

If I want to be good as an investor, then I need to be good at arithmetic to analyse the odds of an investment. If I invest $100 in each trade instead investing $10000 in a single trade then I can make at least 100 trades. That is the number of times that the share prices will go up in a 100 trades is near 33(assuming the probability of share price going up to be 1/3). This is like throwing a coin a hundred times and the number of times that I will get a head in a 100 throws is near to 50. That is how a professional investor makes use of technical analysis to increase the odd of winning.

2) What is Normal distribution?

A probability distribution that plots all of its values in a symmetrical fashion and most of the results are situated around the probability's mean.

The canter contains the greatest number of a value and therefore would be the highest point on the arc of the line. This point is referred to the mean but in simple terms it is the highest number of occurrences of an element.

3) What is Brownian Motion and its relation to Finance?

Brownian motion is the zig-zagging motion exhibited by a small particle immersed in a liquid or gas. The Brownian motion models for financial markets suggest that financial assets have continuous price evolving continuously in time and are driven by Brownian motion processes.

4) What is stochastic calculus in finance ?

Stochastic calculus operates on collection of random variables. An important application of stochastic calculus is in quantitative finance, in which asset prices are often assumed to follow stochastic differential equation.