Mathestate

mathestate (an all lower-case word) is a collaboration of mathematicians and financial economists interested in modeling how extreme events affect asset values. The acronym "mathestate" acknowledges that all rational decisions regarding estate building, preservation or planning are or should be grounded in sound mathematics. Participation, offered and encouraged at www.mathestate.com, currently involves a large number of investigators in various stages of academia in several countries.
The approach follows "heavy tailed" or "fat tailed" methodologies described by Paul Lévy and developed by Bachelier, Mandelbrot and Nolan generally known as Levy-stable distributions or simply stable distributions.
The site is divided into the two major categories people invest in: real estate and financial assets. Modeling of each category is tailored to the pecularities of each domain. Real estate returns are considered in the environment of entreprenurial and control issues. Financial asset returns are approached by exhaustive testing of available data.
A central emphasis in mathestate is risk management. Specifically rejected as inadequate are the convenient, closed form, solutions comprising the dominant paradigm taught in most MBA programs. Examples of these are Value at Risk and the use of the normal distribution. Rather, risk management methodologies described at mathestate employ numerically intensive solutions that rely on the Generalized Central Limit Theorem (GCLT). While the Central Limit Theorem (CLT) is known to every first year statistics student, the GCLT holds that if a distribution has a limiting distribution it must be a member of the stable class. A distribution having such a characteristics leads to a number of useful, interesting and powerful results, the most important of which is to include rather than exclude the effect of extreme values in the distribution.
Financial asset returns appear to be well fit by a lognormal stable (LNS) distribution.
Development of models is conducted on the mathematica platform. The site has extensive tutorials and files in Mathematica which may be downloaded free. Many of the models discussed may be viewed in interactive form at the Wolfram Demonstrations Project.
History
mathestate was created in 2001 as an interactive teaching tool used at San Diego State University by Roger J. Brown, PhD. Conceived of as a way to introduce students and practitioners to the use of data in the analysis of real estate investment decisions, it soon ran into difficulties due to unavailability of data
In 2003 Robert Rimmer, MD, began making contributions to the newly created financial side of mathestate using models that relied on ubiquitous data from securities trading. Today the primary emphasis of mathestate is the further exploration of extreme value models developed by Dr. Rimmer.
Real estate
Presently all real estate models are available at no cost from the Wolfram Demonstration site. Categories of real estate models include
Land use models
Investment analysis
Risk analysis
Financial
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