1 / 11

Actuarial Applications of Multifractal Modeling 1 Introduction and Spatial Applications John A. Major, ASA, MAAA Guy Car

Actuarial Applications of Multifractal Modeling 1 Introduction and Spatial Applications John A. Major, ASA, MAAA Guy Carpenter & Co., Inc. Background. A new paradigm Fractals -- early ‘80s. Multifractals -- late ‘80s to early ‘90s. Applies to: financial time series (Mandelbrot)

trey
Download Presentation

Actuarial Applications of Multifractal Modeling 1 Introduction and Spatial Applications John A. Major, ASA, MAAA Guy Car

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Actuarial Applications of Multifractal Modeling 1 Introduction and Spatial Applications John A. Major, ASA, MAAA Guy Carpenter & Co., Inc.

  2. Background • A new paradigm • Fractals -- early ‘80s. • Multifractals -- late ‘80s to early ‘90s. • Applies to: • financial time series (Mandelbrot) • rain, clouds, etc. (Schertzer & Lovejoy) • population density (Appleby) • insured property values (Lantsman, Major & Mangano)

  3. What is a multifractal? • A type of intensity field • e.g., dollars exposed per square mile • e.g., number of hailstones per square foot • Exhibits “scale-invariance” • Statistically self-similar at various scales • How to simulate • multiplicative cascade

  4. Example multifractal field Population Density in the Northeast USA

  5. The K(q) curve summarizes moment scaling “Trace Moment Graph” shows how the qth-moment scales with resolution. Each q yields a different slope K for the relation. The relation between q and K reveals the multifractal nature of the field. q = 1.4 K = 0.273

  6. Universality (CLT for multifractals) It is thought that a 2-parameter family of generating distributions make up the “central limit” of random multifractals.

  7. Generate: multiplicative cascade 2.0 1.4 “Building block” distribution has average density = 1 0.6 0.0

  8. Application: portfolio allocation Poisson Model Actual Portfolio Multifractal Model

  9. Hail Swath Simulation

  10. Multiple Realizations of Hail Swath

  11. Actuarial Applications of Multifractal Modeling 1 Introduction and Spatial Applications John A. Major, ASA, MAAA

More Related