1. Some specific density functions of aggregated discounted claims with dependent risks
- Author
-
Gemai Chen and Zhehao Zhang
- Subjects
Arrival process ,Applied Mathematics ,Dependent risks ,Poisson process ,Mixed Poisson process ,Specific density ,Exponential function ,Cox process ,symbols.namesake ,Mixing ,Generalized Pareto distribution ,QA1-939 ,symbols ,Applied mathematics ,Beta (velocity) ,Special functions and transforms ,Discounted claims ,Mathematics ,Mixing (physics) - Abstract
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.
- Published
- 2021