6.5 Pricing Stock Options.
In this section we shall consider stock options that give the holder the right to buy a certain stock at a
certain price at a certain future time. The ones we consider are a simplified version of more common
options that give th
6.3 Diffusion and Brownian Motion.
Brownian motion is a probablistic model of certain types of motion. For example
Diffusion of particles in gases, e.g. diffusion of water molecules in air
Diffusion of particles in liquids, e.g. diffusion of sugar m
5.3 Finite Capacity Queues.
The previous sections considered queues with unlimited capacity. In this section we extend the analysis
to queues with finite capacity. This model is useful in situations when potential customers decide not to
join the queue if
6.4 Geometric Brownian Motion.
When we model a stock price X(t) using Brownian motion we have to take into account the fact that the
magnitude of a stock's price has an effect on how it changes. For example a 25 increase in the price of
a stock whose curr
An important application of continuous time Markov processes is to queues. A queue is a waiting line.
For example, the people waiting in line to place an order at McDonalds is a queue. Typically, for a
queue we are interested in things like the a
5.4 Queuing Networks.
Queuing networks are models of situations where the customers have to go through several stages and
may have to wait in line at each stage. We illustrate the principles by means of an example.
Example 1. At a certain shop jobs requir