Skip to Main Content
An Introduction to Financial Markets
book

An Introduction to Financial Markets

by Paolo Brandimarte
November 2017
Beginner content levelBeginner
784 pages
22h 31m
English
Wiley
Content preview from An Introduction to Financial Markets

Chapter Fifteen Optimization Model Building

In this chapter, we describe a range of optimization models aimed at financial applications. Emphasis will be almost exclusively on model building, rather than model solving, which is deferred to the next chapter. To this aim, it is important to have a broad and clear picture of the types of model formulations that may be solved by available software tools. Intuition suggests that a large problem is a harder nut to crack than a small one and that a linear problem is easier than a nonlinear one. Actually, this is not necessarily true, and we shall learn that the main problem feature, drawing the line between relatively easy and difficult problems, is convexity.

We begin, in Section 15.1, with a classification of optimization problems, revolving around the concepts of convex sets and convex functions. The impor tant class of linear programming (LP) models is the topic of Section 15.2. We have already appreciated the role of LP models in the mathematics of arbitrage in Section 2.4. Here, we see how it may be an essential tool in solving possibly large-scale problems. The next level of the hierarchy is convex quadratic programming (QP), which is dealt with in Section 15.3. Convex QP models are the foundation of the mean–variance portfolio theory illustrated in Chapter 8. In Section 15.4, we take a detour into the realm of hard, nonconvex problems. While LPs and convex QPs can be solved quite efficiently, here we add an integrality restriction ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Economics for Financial Markets

Economics for Financial Markets

Brian Kettell

Publisher Resources

ISBN: 9781118014776Purchase book