Math

Question 1

Sum of arithmetic sequence

Answer 1

n/2(2a + (n-1)d) –> d=distance, a=1st element, n=number of elements

Question 2

∏

Answer 2

This symbol represents the product operator, analogous to how ∑ represents the summation operator. It indicates that you multiply a sequence of terms together.

Question 3

cumulative return compounding vs. cumulative return rebalancing

Answer 3

Question 4

Exponential Function

Answer 4

A mathematical function that grows faster than any polynomial function. The base of the exponential function, e, is approximately equal to 2.71828, and it’s a fundamental constant in mathematics, similar to π.

Question 5

Taylor series

Answer 5

Taylor series or Taylor expansion: of a function is an a function is an infinite sum of terms that are expressed in terms of the function’s derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century.

Question 6

Stochastic process

Answer 6

a stochastic or random process is a mathematical object usually defined as a sequence of random variables in a probability space, where the index of the sequence often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner

Question 7

Brownian motion

Answer 7

named after the botanist Robert Brown, who first described the phenomenon in 1827, while looking through a microscope at pollen immersed in water. In 1900, the French mathematician Louis Bachelier modeled the stochastic process now called Brownian motion in his doctoral thesis, The Theory of Speculation

Question 8

geometric Brownian motion (GBM)

Answer 8

also known as exponential Brownian motion, is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion with drift.

It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the Black–Scholes model.

Question 9

stochastic differential equation (SDE)

Answer 9

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process.