TOOLS FOR CONTINUOUS-TIME MODELS

The following sections are included:

• Wiener Processes

  • Definition and Background

  • Essential Properties

• Itô Integrals and Processes

  • A Motivating Example

  • Integrals with Respect to Brownian Motions

  • Itô Processes

• Itô's Formula

• Tools for Martingale Pricing

  • Girsanov's Theorem and Changes of Measure

  • Representation of Martingales

• Tools for Discontinuous Processes

  • “J” Processes

  • More General Processes