Mathematics (Apr 2023)

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

  • Kang Hu,
  • Ya Huang,
  • Yingchun Deng

DOI
https://doi.org/10.3390/math11091994
Journal volume & issue
Vol. 11, no. 9
p. 1994

Abstract

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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