What “Convoluted Expression” Means in Mathematical Finance

Summary

The document clarifies the phrase “convoluted expression” in a discussion of copula estimation using financial return distributions. The quoted context says full maximum likelihood can be difficult because of dimensionality and because the copula parameter may be expressed in terms of the marginal distribution parameters. The question asks whether “convoluted” has a specialized mathematical meaning there.

The answer says the phrase is ordinary descriptive language for an expression that is complicated, cumbersome, or messy to handle. It distinguishes that usage from convolution, the mathematical operation on functions: despite the similar wording, the operation is unrelated to the author’s phrase. This resolves a terminology question but does not explain the copula model, derive a likelihood, or show how marginal parameters affect a copula parameter. The discussion is therefore useful for reading the cited modeling text, while offering no technical method for estimating copulas or assessing the practical consequences of a complicated parameter relationship.

Key ideas

• In the cited context, “convoluted expression” means a complicated or cumbersome formula.
• The phrase is ordinary descriptive language rather than a specialized term in mathematical finance.
• Convolution is a separate mathematical operation and is unrelated to this use of “convoluted.”
• The answer clarifies terminology but does not provide a copula estimation method.

Tags

# Is there a specific meaning to the word "convoluted" in maths or mathematical finance?


# Is there a specific meaning to the word "convoluted" in maths or mathematical finance?












I'm reading about copula estimation in the book Financial Modeling Under Non-Gaussian Distributions by Jondeau, Poon and Rockinger. They say that full maximum likelihood can be difficult because of i) dimensionality and because ii) "the copula parameter may be a "convoluted expression" of the margins parameter."

I've been looking for a translation of that word, but I only find difficult or complicated as synonyms of convoluted. I believe there is more to it than just "complicated". Is there maybe a more specific meaning for this word? Would you know what the authors mean with "convoluted expression" in this context?

## Answer by Alex C (score 2)

https://quant.stackexchange.com/a/29758

"convoluted expression" in American usage just means a complicated, big mathematical expression, sometimes also called "hairy" or "messy". It is ugly to work with and to look at, so you prefer not to deal with it if possible. Nothing more than that.

There is also a mathematical operation called "convolution ("Faltung" in German) but it has nothing to do with the other meaning. When convolution is applied to two functions they are said to be "convolved" which is a different word altogether.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.