INFINITE VARIANCE DISTRIBUTION IN FINANCE AND INSURANCE

Kamal Boukhetala¹, Amel Laouar²* and Rachid Sabre^3
1Prof. Dr., Universityof science and technology Houari Boumedienne (USTHB), Algiers, Algeria, kboukhetala@usthb.dz
²Assist. Prof. Phd., Hight scool of marine Sciences and coastal planning(ENSSMAL), Algiers, Algeria, amel.laouar@gmail.com
*Corresponding Author

Abstract

In insurance as in finance, risk management is very important. And that starts with the right choice of mathematical models used in order to make the best decisions. In the financial markets, the study and modelling of returns is crucial, as it is also important for an insurance company to properly model risk and claims amount. For a long time, the Gaussian process and variables have been studied and their usefulness in stochastic and statistical modelling is well accepted, like the Black-Scholes in finance and Cramér-Lundberg model in insurance. However, they don't allow for large fluctuations and may sometimes be inadequate for modelling high variability.

One of the most important questions in both cases is whether the variance of returns (or claims) is finite or infinite. In other words, we need to know if we are in the presence of heavy tail distribution or not.

That's why it's important to focus on other family of laws and processes such as stable random variable’s and processes which naturally appear as alternative modelling tools. There are several reasons which have led us to choose the stable distributions, they are a very rich class of probability distributions can represent different asymmetries and heavy tails.
in this work we will present various graphical statistical tests which will allow us to verify whether we are in the presence of an infinite variance variables  or not, and especially if we have a alpha  stable distribution

Keywords: Stable distribution, Infinite variance, Simulation, Statistical tests.

REFERENCE LIST
V.M. Zolotarev and V. Uchaikin (1999)., Chance and stability :  Stable distribution and their application. Modern probability and statistics. Netherlands, Utrecht, VSP. Tokyo, Japan
A. Janiko and A. Weron  (1994)., Simulation and chaotic behavior of α-stable process. Marcel Dekker, INC, New York