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Optimal Probability Density Function Models for Stochastic Model Outcomes: Parametric Model Fitting on Tail Distributions

Y. Chueha
Organization: Central Washington University, Ellensburg, WA
Department: Department of Mathematics
W. Curtis

2004 International Mathematica Symposium
Conference location

Banff, Canada

This paper documents a Mathematica-related development activity in the category of applied mathematics for the field of Actuarial Science. This is an on-going research project sponsored by a Central Washington University Seed Grant subsequent to the papers [Longley-Cook 2003 and Chueh 2002] on efficient stochastic modeling techniques. Efficient stochastic modeling for the insurance business can be achieved by effective sampling of stochastic economic (risk) scenarios. The run-time can be significantly reduced and the model outcome distribution can be preserved on the critical tails. However, there is a lack of a well-known software applications to help modelers analyze the model outcome distribution. This research will apply Mathematica as the main programming and computational resource to develop a user-friendly Mathematica application AMOOF (Actuarial Model Outcome Optimal Fit) that finds the best parametric probability density model for given stochastic model data. The AMOOF application will carry out a series of parametric probability model fitting processes and then create mathematical reports for actuaries. Unlike other commercial statistical data fitting packages, a comprehensive inventory of special and mixed distributions will be used to enhance fitting accuracy on the tails. The project will utilize Mathematica's capabilities in calculus, graphing, and optimization and, when complete, will be valuable for actuarial modeling that is critical for a company's capital determination, reserve setting, risk analysis, and product pricing.

*Business and Economics
*Mathematics > Probability and Statistics

Optimal Probability Density Function, Stochastic Model, Parametric Model Fitting, Tail Distributions, Actuarial Model Outcome Optimal Fit, AMOOF, Actuarial Science, stochastic modeling techniques
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