4.2.3 Risk-Neutral Measure
- 1. Geometric Brownian Motion. Consider an economy consisting of a risk-free asset and a stock price (risky asset). At time , the risk-free asset and the stock price have the following diffusion processes
where is the risk-free rate, is the stock price drift rate, is the stock price volatility(which are all time dependent) and is a -standard Wiener process on the probability space .
From the following discounted stock price process
show, using Girsanov's theorem, ...