Approximations of Weyl fractional-order integrals with insurance applications
Chengxiu Ling, Zuoxiang Peng
TL;DR
This paper develops methods to approximate Weyl fractional-order integrals and applies these to risk measures in extreme value theory, providing practical examples and numerical validation.
Contribution
It introduces new approximation techniques for Weyl fractional integrals and applies them to risk measures in extreme value analysis.
Findings
Effective higher-order tail approximations for deflated risks
Improved approximations for Haezendonck-Goovaerts risk measures
Numerical results demonstrating the accuracy of the methods
Abstract
In this paper, we investigate the approximations of generalized Weyl fractional-order integrals in extreme value theory framework. We present three applications of our asymptotic results concerning the higher-order tail approximations of deflated risks as well as approximations of Haezendonck-Goovaerts and expectile risk measures. Illustration of the obtained results is done by various examples and some numerical analysis.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Stochastic processes and financial applications · Insurance and Financial Risk Management