Random Equity Returns

Overview

The standard quantitative model of equities is the Geometric Brownian Motion. (see quantitative equity modeling).

• {% \mu %} - the arithmetic average return
• {% \sigma %} - the volatility

The analysis assumes that there is an equity index that the retiree has their money invested in. That is, we ignore the fact that the retiree could be investing in multiple different stocks and just approximate it by a single index.

Topics

• Simulating an Ito Process - the simplest way to simulate an equity is to assume a constant growth rate and a volatility.
• Simulating a Brownian Bridge - the brownian bridge