Results in Applied Mathematics (Aug 2021)

Some specific density functions of aggregated discounted claims with dependent risks

  • Zhehao Zhang,
  • Gemai Chen

Journal volume & issue
Vol. 11
p. 100168

Abstract

Read online

This paper obtains some specific density functions for aggregated discounted claims where the claim amounts are dependent, or the inter-claim times are dependent, or the claim amounts and the claim arrival process are both dependent. The dependence is structured through mixing, and the claim arrival process studied is either an ordinary Poisson process or a mixed Poisson process. Closed form densities are obtained for gamma, generalized exponential, generalized Pareto and beta mixing, and an important use of them is illustrated.

Keywords