Feeds:
Posts

## easier generalization: second parameter in Mittag-Leffler function?

 Inbox x

### Zulfikar Ahmed<wile.e.coyote.006@gmail.com>

5:21 PM (0 minutes ago)

 to David, bcc: aimee
Sir,

Attached is a nice exposition of the role of Mittag-Leffler functions in ‘fractional modeling’.  Our findings to date suggest power law is not good enough for volatility EN(t), and so my first model was too broad perhaps and quite possibly the mathematics of this function has natural modeling ability not yet explored.  Therefore this is my modified conjecture, to tweak the second parameter of these Mittag-Leffler functions to try to fit the empirical volatility data.  Attached both computational methods for E_{a,b}(z) as an entire function as well as rationales.  Right now my task is to find some libraries for R and perhaps revisit complex analysis since it’s been many years I did a single residue calculation.

I am preparing to translate MATLAB code to R for this next phase where we ask whether tweaking 0<a<1 for E_{a,b}(z) for the Mittag-Leffler is sufficient to account for the discrepancy seen in the attached residue from power law log-log line fit.

6 Attachments

Preview attachment residuals-log-log-volatility-shocks.png

residuals-log-log-volatility-shocks.png

Preview attachment fractional-modeling-mittag-leffler.pdf

fractional-modeling-mittag-leffler.pdf

Preview attachment mathematics-03-00368.pdf

mathematics-03-00368.pdf

Preview attachment mittag-leffler-type-functions-zeros-and-growth.pdf

mittag-leffler-type-functions-zeros-and-growth.pdf

Preview attachment computation-mittag-leffler-functions.PDF

computation-mittag-leffler-functions.PDF

Preview attachment graphical-interpretation-mittag-leffler.pdf

graphical-interpretation-mittag-leffler.pdf