# Monthly Archives: March, 2016

Updating the Cholesky factorization of $A'A=LL'$ when one or more columns are added to or removed from matrix $A$ can be done very efficiently obviating the re-factorization from scratch. Continue reading →

# Zero risk

What does it mean for a random variable to exhibit zero risk? It of course depends on the risk measure we are using to quantify it. Continue reading →

# Average value-at-risk of simple quadratic form

The average value-at-risk of a quadratic form $y'y$, where $y\sim \mathcal{N}(0_n,I_n)$ is given by a particularly complex closed-loop formula which I’ll describe below.

# Strict monotonicity of expected shortfall

The expected shortfall, also known as average value-at-risk or conditional value-at-risk, is a coherent risk measure defined as

$\mathrm{AV@R}_{\alpha}[Z]=\inf_{t\in\mathbb{R}} \{t+\alpha^{-1}\mathbb{E}[Z-t]_+\}$

for $Z\in\mathcal{Z}:=\mathcal{L}_p(\Omega,\mathcal{F},\mathrm{P})$ for some $p\in[1,+\infty]$.

mathbabe

Exploring and venting about quantitative issues

Look at the corners!

The math blog of Dmitry Ostrovsky

The Unapologetic Mathematician

Mathematics for the interested outsider

Almost Sure

A random mathematical blog

Mathematix

Mathematix is the mathematician of the village of Asterix