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Uncertainty Claim Pricing using Weibull Distortion Operator Bright O.Osu, Obiageri E.Ogwo and Silas A. Ihedioha Volume 21 (July, 2012), pp 73 – 78
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Uncertainty Claim Pricing using Weibull Distortion Operator

by

Bright O.Osu, Obiageri E.Ogwo  and  Silas A. Ihedioha

Department of Mathematics , Abia State University, Uturu, Nigeria.

Abstract

In this paper, we consider the problem of uncertainty Claim Pricing using Distortion Operators. This approach was first developed in Insurance Pricing, where the original distortion function was defined in terms of the normal distribution. We generalize this approach by using a distortion that is based on the Weibull distribution. The Weibull family allows for heavier and skewed tail because it is so flexible that other statistical distributions can be recovered from it by change of parameters. The problem of uncertainty Claims has been extensively studied for non-Gaussian model in which the formula was derived for the NIG asset pricing. We show here how Weibull based distortion function can be used to derive the formula for asset pricing of uncertainty future returns of a risky asset. We derive also the risk measure for the incurred risk modeled by the Weibull variables and show that it follows the power law.

Keywords: Uncertainty claim, Weibull distribution, Insurance pricing, Power law.

MSC: 91G10

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