Estimating the Gerber–Shiu Function in the Two-Sided Jumps Risk Model by Laguerre Series Expansion

Kang Hu, Ya Huang () and Yingchun Deng ()
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Kang Hu: Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
Ya Huang: School of Business, Hunan Normal University, Changsha 410081, China
Yingchun Deng: School of International Business, Hunan University of Information Technology, Changsha 410151, China

Mathematics, 2023, vol. 11, issue 9, 1-30

Abstract: In this paper, we consider an insurance risk model with two-sided jumps, where downward and upward jumps typically represent claim amounts and random gains, respectively. We use the Laguerre series to expand the Gerber–Shiu function and estimate it based on observed information. Moreover, we show that the estimator is easily computed and has a fast convergence rate. Numerical examples are also provided to show the efficiency of our method when the sample size is finite.

Keywords: two-sided jumps; Gerber–Shiu function; Laguerre series; estimator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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