Monthly Archives: March, 2016

Cholesky updates of A’A

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 →

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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.

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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].

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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