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* README update

* mathbb fix attempt

* poetry updates
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antonvorobets authored Aug 27, 2024
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15 changes: 11 additions & 4 deletions README.md
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Expand Up @@ -29,13 +29,19 @@ Entropy Pooling is a powerful method for implementing subjective views and
performing stress-tests for fully general Monte Carlo distributions. It was first
introduced by [Meucci (2008)](https://ssrn.com/abstract=1213325) and refined
with sequential algorithms by [Vorobets (2021)](https://ssrn.com/abstract=3936392).

[You can loosely think about Entropy Pooling as a generalization of the Black-Litterman model](https://antonvorobets.substack.com/p/entropy-pooling-vs-black-litterman-abb608b810cd) without all the oversimplifying assumptions. Entropy Pooling operates directly on
[the next generation market representation](https://youtu.be/4ESigySdGf8?si=yWYuP9te1K1RBU7j&t=46)
defined by the simulation matrix $R\in \mathbb{R}^{S\times I}$ and associated joint
scenario probability vector $p\in \mathbb{R}^{S}$.

For a quick introduction to Entropy Pooling intuition, watch [this YouTube video](https://youtu.be/qk_5l4ICXfY).

The original Entropy Pooling approach solves the minimum relative entropy problem

$$q=\underset{x}{\text{argmin}}\lbrace x^{T}\left(\ln x-\ln p\right)\rbrace$$

subject to the constraints
subject to linear constraints on the posterior probabilities

$$Gx\leq h \quad \text{and} \quad Ax=b.$$

Expand All @@ -45,8 +51,9 @@ changing the joint scenario probabilities from a prior probability vector $p$
to a posterior probability vector $q$.

A useful statistic when working with Entropy Pooling is the effective number of
scenarios introduced by [Meucci (2012)](https://ssrn.com/abstract=1971808). For
a causal Bayesian nets overlay on top of Entropy Pooling, see
scenarios introduced by [Meucci (2012)](https://ssrn.com/abstract=1971808).

For a causal Bayesian network overlay on top of Entropy Pooling, see
[Vorobets (2023)](https://ssrn.com/abstract=4444291).

Video walkthroughs
Expand All @@ -55,7 +62,7 @@ Video walkthroughs
Video walkthroughs of the two notebook examples are available [here](https://youtu.be/hDt103zEML8)
and [here](https://youtu.be/DK1Pv5tuLgo). The videos give additional insights into
Entropy Pooling theory and its sequential refinements. It is highly recommended
to watch these two videos to quickly increase your understanding.
to watch these videos to quickly increase your understanding.

Portfolio Construction and Risk Management Book
-----------------------------------------------
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109 changes: 64 additions & 45 deletions poetry.lock

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2 changes: 1 addition & 1 deletion pyproject.toml
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[tool.poetry]
name = "entropy-pooling"
version = "1.0.6"
version = "1.0.7"
description = "Entropy Pooling in Python with a BSD 3-Clause license."
authors = ["Fortitudo Technologies <[email protected]>"]
license = "BSD-3-Clause"
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