17-12-15-(15)-14-(14)
Portfolio Optimization
2.5 Asset Structure
In the previous sections we were looking at single stock and time and asking “Can yesterday predict today?”. Which is realm of Machine #1, which we try to get μ\mu and ∑\sum,…
2.4 Temporal Structure
The other question is: is the stock market a completely random casino, or are there hidden patterns we can predict?, in math jargon terms: If the market is i.i.d.,…
2.3 Non-Gaussianity
Vanilla Markowitz assumes that the stock market behaves like a perfect bell curve, which also known as Gaussian (Normal) Distribution: Gaussian Distribution is very useful for explaining physical concepts…
Optimization
Unconstrained Optimization
In unconstrained optimization, we minimize an objective function that depends on real variables, and these variables have no restrictions. where x∈ℝnx \in \mathbb{R}^n is a real vector with n≥1n \ge 1 components and f:ℝn→ℝf : \mathbb{R}^n \to \mathbb{R} is a smooth function. A Simple Example Local Minimizer Local minimizer is a point that achieves the…
Introduction to Optimization
In mathematics, computer science, and operations research, Optimization simply means picking the absolute best element from a set of available alternatives. Whether you are an electricity provider figuring out how many power plants to build, or a warehouse manager trying to shorten the distance your workers walk, you are trying to optimize. But how do computers and mathematicians do…