Semiparametric estimation in the optimal dividend barrier for the classical risk model

Research output: Contribution to journalArticle

Abstract

In the context of an insurance portfolio which provides dividend income for the insurance company’s shareholders, an important problem in risk theory is how the premium income will be paid to the shareholders as dividends according to a barrier strategy until the next claim occurs whenever the surplus attains the level of ‘barrier’. In this paper, we are concerned with the estimation of optimal dividend barrier, defined as the level of the barrier that maximizes the expected discounted dividends until ruin, under the widely used compound Poisson model as the aggregate claims process. We propose a semi-parametric statistical procedure for estimation of the optimal dividend barrier, which is critically needed in applications. We first construct a consistent estimator of the objective function that is complexly related to the expected discounted dividends and then the estimated optimal dividend barrier as the minimizer of the estimated objective function. In theory, we show that the constructed estimator of the optimal dividend barrier is statistically consistent. Numerical experiments by both simulated and real data analyses demonstrate that the proposed estimators work reasonably well with an appropriate size of samples.

Original languageEnglish
Pages (from-to)845-862
Number of pages18
JournalScandinavian Actuarial Journal
Volume2018
Issue number9
DOIs
Publication statusPublished - 2018 Oct 21

Keywords

  • Beekman’s convolution series
  • Semiparametric estimation
  • compound poisson
  • dividend
  • ruin theory
  • statistical estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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