Actuarial Applications of Multifractal Modeling Part I: Introduction and Spatial Applications

Special Topics (narrow topic or advanced); Multifractals are mathematical generalizations of fractals, objects displaying "fractional dimension," "scale invariance," and "self-similarity." Many natural phenomena, including some of considerable interest to the casualty actuary (meteorological conditions, population distribution, financial time series), have been found to be well-represented by (random) multifractals. In this part I paper, we define and characterize multifractals and show how to fit and simulate multifractal models in the context of two-dimensional fields. In addition, we summarize original research we have published elsewhere concerning the multifractal distribution of insured property values, and discuss how we have used those findings in particular and multifractal modeling in general in a severe storm catastrophe model.