Large Deviations Theory and Its Potential Uses in Finance

Summary

The document introduces large deviations theory as a study of the remote tails of probability distributions, especially how tail behavior changes as a parameter grows. It contrasts this focus with the central limit theorem, which describes behavior around the mean, and asks what the growing parameter represents in relevant financial settings. It also asks which practical financial models use the theory and whether it produces a widely used risk measure comparable to expected shortfall.

No applications, derivations, or answers are provided; the text is a research question rather than an explanation of a technique. It therefore does not establish a specific large-deviation metric or demonstrate how to use one in portfolio or market risk analysis. Its useful contribution is framing the distinction between central behavior and rare-event tails, while leaving the financial interpretation and practical use unresolved.

Key ideas

• Large deviations theory studies the probabilities of remote tail events in distributions or sequences of distributions.
• The document contrasts tail behavior with the central behavior described by the central limit theorem.
• It asks what parameter grows in financial applications but does not resolve that question.
• No practical model, risk metric, or worked financial application is presented.

Tags

# Large deviations theory in finance


# Large deviations theory in finance












In probability theory, the theory of large deviations concerns the asymptotic behavior of remote tails of sequences of probability distributions.

A related post says:

> Large deviations theory is concerned with the behavior of the tails of the distribution of a r.v. as a parameter N becomes large. The Central Limit theorem tells you what happens to the mean, the LD Theory tells you about the tails.

Not sure what $N$ refers to that becomes large, but what are some common and practical applications of large deviations theory in finance? (Practical as in usable within a well-known financial model, as opposed to theoretical, pointless meanderings about stochastic process behaviors.)

Or better, what is the most popular measure or metric put out by large deviations theory (in the same way that the measure called expected shortfall (CVaR) was borne from extreme value theory)?

Please no links to papers from google search unless you plan to explain what those papers actually contain.

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