September 2013
Intermediate to advanced
336 pages
9h 47m
English
Content preview from A Workout in Computational Finance
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,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
16 Optimization Techniques
Efficient numerical optimization techniques play a key role in many of the calculation tasks in modern financial mathematics. Optimization problems occur for example in asset allocation, risk management and model calibration problems.
From a more theoretical point of view, the problem of finding an x* ∈ ℝn that solves
is called an optimization problem for a given function f (x) : ℝn → ℝ. The function f is called the objective function and S is the feasible region. When S is empty, the problem is called infeasible. If it is possible to find a sequence x0 ∈ S, x1 ∈ S, ... such that f(xk) → −∞ for k → ∞, then the problem is called unbounded. For problems that are neither infeasible nor unbounded it may be possible to find a solution x* satisfying
Such an x* is called a global minimizer of the optimization problem (16.1) (see Figure 16.1).1
On some occasions, one may only find an x* satisfying
where 
is an open sphere with radius 
and midpoint x*. In this case, ...
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.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.